Threshold graph limits and random threshold graphs (2009)
Persi Diaconis, Susan Holmes, Svante Janson
Abstract. We study the limit theory of large threshold graphs and apply this to a variety of models for random threshold graphs. The results give a nice set of examples for the emerging theory of...
Functions of random walks on hyperplane arrangements (2009)
Athanasiadis, Christos A., Diaconis, Persi
Many seemingly disparate Markov chains are unified when viewed as random walks on the set of chambers of a hyperplane arrangement. These include the Tsetlin library of theoretical computer science...
THE MARKOV CHAIN MONTE CARLO REVOLUTION (2009)
Abstract. The use of simulation for high-dimensional intractable computations has revolutionized applied mathematics. Designing, improving and understanding the new tools leads to (and leans on)...
A rule of thumb for riffle shuffling (2009)
Assaf, Sami, Diaconis, Persi, Soundararajan, K.
We study how many riffle shuffles are required to mix n cards if only certain features of the deck are of interest, e.g. suits disregarded or only the colors of interest. For these features, the...
Threshold graph limits and random threshold graphs (2009)
Diaconis, Persi, Holmes, Susan, Janson, Svante
We study the limit theory of large threshold graphs and apply this to a variety of models for random threshold graphs. The results give a nice set of examples for the emerging theory of graph limits.
Persi Diaconis, Susan Holmes, Richard Montgomery
Abstract. We analyze the natural process of flipping a coin which is caught in the hand. We show that vigorously flipped coins tend to come up the same way they started. The limiting chance of coming...
OF INDEPENDENT GAMMA RANDOM VARIABLES (2009)
Persi Diaconis, Michael D. Perlman
The tail probabilities of two weighted sums of independent gamma random variables are compared when the first vector of weights majorizes the second vector of weights. The conjecture that the two...
Riffle shuffles of a deck with repeated cards (2009)
Assaf, Sami, Diaconis, Persi, Soundararajan, K.
We study the Gilbert-Shannon-Reeds model for riffle shuffles and ask 'How many times must a deck of cards be shuffled for the deck to be in close to random order?'. In 1992, Bayer and Diaconis gave a...
On adding a list of numbers (and other one-dependent determinantal processes) (2009)
Borodin, Alexei, Diaconis, Persi, Fulman, Jason
Adding a column of numbers produces "carries" along the way. We show that random digits produce a pattern of carries with a neat probabilistic description: the carries form a one-dependent...
FASTEST MIXING MARKOV CHAIN ON GRAPHS WITH SYMMETRIES (2009)
Xiao, Lin, Diaconis, Persi, Boyd, Stephen, Parrilo, Pablo A.
We show how to exploit symmetries of a graph to efficiently compute the fastest mixing Markov chain on the graph (i.e., find the transition probabilities on the edges to minimize the second-largest...
Carries, shuffling, and symmetric functions (2009)
Diaconis, Persi, Fulman, Jason
The "carries" when n random numbers are added base b form a Markov chain with an "amazing" transition matrix determined by Holte. This same Markov chain occurs in following the number of descents or...
On characterizations of Metropolis type algorithms in continuous time (2009)
Diaconis, Persi, Miclo, Laurent
In the continuous time framework, a new definition is proposed for the Metropolis algorithm $(\wi X_t)_{t\geq0}$ associated to an a priori given exploratory Markov process $( X_t)_{t\geq0}$ and to a...
On barycentric subdivision (2009)
Diaconis, Persi, Miclo, Laurent
Consider the barycentric subdivision which cuts a given triangle along its medians to produce six new triangles. Uniformly choosing one of them and iterating this procedure gives rise to a Markov...
On characterizations of Metropolis type algorithms in continuous time (2009)
Diaconis, Persi, Miclo, Laurent
In the continuous time framework, a new definition is proposed for the Metropolis algorithm $(\wi X_t)_{t\geq0}$ associated to an a priori given exploratory Markov process $( X_t)_{t\geq0}$ and to a...
On barycentric subdivision (2009)
Diaconis, Persi, Miclo, Laurent
Consider the barycentric subdivision which cuts a given triangle along its medians to produce six new triangles. Uniformly choosing one of them and iterating this procedure gives rise to a Markov...
On characterizations of Metropolis type algorithms in continuous time (2009)
Diaconis, Persi, Miclo, Laurent
In the continuous time framework, a new definition is proposed for the Metropolis algorithm $(\wi X_t)_{t\geq0}$ associated to an a priori given exploratory Markov process $( X_t)_{t\geq0}$ and to a...
On barycentric subdivision (2009)
Diaconis, Persi, Miclo, Laurent
Consider the barycentric subdivision which cuts a given triangle along its medians to produce six new triangles. Uniformly choosing one of them and iterating this procedure gives rise to a Markov...
On characterizations of Metropolis type algorithms in continuous time (2009)
Diaconis, Persi, Miclo, Laurent
In the continuous time framework, a new definition is proposed for the Metropolis algorithm $(\wi X_t)_{t\geq0}$ associated to an a priori given exploratory Markov process $( X_t)_{t\geq0}$ and to a...
On barycentric subdivision (2009)
Diaconis, Persi, Miclo, Laurent
Consider the barycentric subdivision which cuts a given triangle along its medians to produce six new triangles. Uniformly choosing one of them and iterating this procedure gives rise to a Markov...
ADVANCES IN APPLIED MATHEMATICS 4, 175- 196 ( 1983) The Mathematics of Perfect Shuffles (2008)
Persi Diaconis, R. L. Graham, William M. Kantor
There are two ways to perfectly shuffle a deck of 2n cards. Both methods cut the deck in half and interlace perfectly. The out shuffle 0 leaves the original top card on top. The in shuffle I leaves...
The Solutions to Elmsley’s Problem (2008)
We give a formula for the optimal sequence of perfect shuffles to bring a card at position p to the top (or indeed, to any position). This solves a fifty-year-old problem of Elmsley. The argument...
S:intro secA GRAPH LIMITS AND EXCHANGEABLE RANDOM GRAPHS (2008)
Abstract. We develop a clear connection between deFinetti’s theorem for exchangeable arrays (work of Aldous–Hoover–Kallenberg) and the emerging area of graph limits (work of Lovász and many...
Horseshoes in multidimensional scaling and local kernel methods (2008)
Diaconis, Persi, Goel, Sharad, Holmes, Susan
Classical multidimensional scaling (MDS) is a method for visualizing high-dimensional point clouds by mapping to low-dimensional Euclidean space. This mapping is defined in terms of eigenfunctions of...
Gibbs Sampling, Exponential Families and Orthogonal Polynomials (2008)
Diaconis, Persi, Khare, Kshitij, Saloff-Coste, Laurent
We give families of examples where sharp rates of convergence to stationarity of the widely used Gibbs sampler are available. The examples involve standard exponential families and their conjugate...
Rejoinder: Gibbs Sampling, Exponential Families and Orthogonal Polynomials (2008)
Diaconis, Persi, Khare, Kshitij, Saloff-Coste, Laurent
We are thankful to the discussants for their hard, interesting work. The main purpose of our paper was to give reasonably sharp rates of convergence for some simple examples of the Gibbs sampler. We...
Products of Universal Cycles (2008)
Universal cycles are generalizations of de Bruijn cycles to combinatorial patterns other than binary strings. We show how to construct a product cycle of two universal cycles, where the window widths...
Combinatorics for the East model (2008)
Fan Chung, Persi Diaconis, Ronald Graham
We study the number of configurations in the East model of statistical physics. This may be pictured as sites in a line. The site at zero is always occupied. The site at i>0 can only be changed if...
Combinatorics for the East model (2008)
Fan Chung, Persi Diaconis, Ronald Graham
We study the number of configurations in the East model of statistical physics. This may be pictured as sites in a line. The site at zero is always occupied. The site at i>0 can only be changed if...
Carries, Shuffling and An Amazing Matrix (2008)
Diaconis, Persi, Fulman, Jason
The number of ``carries'' when $n$ random integers are added forms a Markov chain [23]. We show that this Markov chain has the same transition matrix as the descent process when a deck of $n$ cards...
Projection pursuit for discrete data (2008)
Diaconis, Persi, Salzman, Julia
This paper develops projection pursuit for discrete data using the discrete Radon transform. Discrete projection pursuit is presented as an exploratory method for finding informative low dimensional...
Probability, Persi Diaconis
Despite a true antipathy to the subject, Hardy contributed deeply to modern probability. His work with Ramanujan begat probabilistic number theory. His work on Tauberian theorems and divergent series...
PATTERNS IN EIGENVALUES: (2008)
Abstract. Typical large unitary matrices show remarkable patterns in their eigenvalue distribution. These same patterns appear in telephone encryption, the zeros of Riemann’s zeta function, a...
ANALYSIS OF A BOSE-EINSTEIN MARKOV CHAIN (2008)
This paper gives sharp rates of convergence to stationarity for a Markov chain generating Bose-Einstein configurations of n balls in k boxes. The analysis leads to curious identities for the arc sine...
Random matrices, magic squares and matching polynomials (2008)
Characteristic polynomials of random unitary matrices have been intensively studied in recent years: by number theorists in connection with Riemann zetafunction, and by theoretical physicists in...
ADVANCES IN APPLIED MATHEMATICS 4, 175- 196 ( 1983) The Mathematics of Perfect Shuffles (2008)
Persi Diaconis, R. L. Graham, William M. Kantor
There are two ways to perfectly shuffle a deck of 2n cards. Both methods cut the deck in half and interlace perfectly. The out shuffle 0 leaves the original top card on top. The in shuffle I leaves...
The Markov moment problem and de Finetti’s theorem (2008)
Persi Diaconis, David Freedman
The Markov moment problem is to characterize sequences s0,s1,s2,...admitting the representation sn = � 1 0 xnf(x)dx, where f(x) is a probability density on [0, 1] and 0 ≤ f(x) ≤ c for almost...
Combinatorics for the East model (2008)
Fan Chung, Persi Diaconis, Ronald Graham
We study the number of configurations in the East model of statistical physics. This may be pictured as sites in a line. The site at zero is always occupied. The site at i>0 can only be changed if...
Gibbs sampling, exponential families and orthogonal polynomials (2008)
Persi Diaconis, Kshitij Khare, Laurent Saloff-coste
Abstract. We give families of examples where sharp rates of convergence to stationarity of the widely used Gibbs sampler are available. The examples involve standard exponential families and their...
Graph limits and exchangeable random graphs (2007)
Diaconis, Persi, Janson, Svante
We develop a clear connection between deFinetti's theorem for exchangeable arrays (work of Aldous--Hoover--Kallenberg) and the emerging area of graph limits (work of Lovasz and many coauthors). Along...
A SUPER-CLASS WALK ON UPPER-TRIANGULAR MATRICES (2007)
Ery Arias-castro, Persi Diaconis, Richard Stanley
Let G be the group of nn upper-triangular matrices with elements in a nite eld and ones on the diagonal. This paper applies the character theory of Andre, Carter and Yan to analyze a natural random...
Running head: Constrained Ising Model. (2007)
We study a one-dimensional spin (interacting particle) system, with product Bernoulli(p) stationary distribution, in which a site can flip only when its left neighbor is in state +1. Such models have...
Fastest mixing Markov chain on graphs with symmetries (2007)
Boyd, Stephen, Diaconis, Persi, Parrilo, Pablo A., Xiao, Lin
We show how to exploit symmetries of a graph to efficiently compute the fastest mixing Markov chain on the graph (i.e., find the transition probabilities on the edges to minimize the second-largest...
On fixed points of permutations (2007)
Diaconis, Persi, Fulman, Jason, Guralnick, Robert
The number of fixed points of a random permutation of 1,2,...,n has a limiting Poisson distribution. We seek a generalization, looking at other actions of the symmetric group. Restricting attention...
Separation cut-offs for birth and death chains (2007)
Diaconis, Persi, Saloff-Coste, Laurent
This paper gives a necessary and sufficient condition for a sequence of birth and death chains to converge abruptly to stationarity, that is, to present a cut-off. The condition involves the notions...
On times to quasi-stationarity for birth and death processes (2007)
Diaconis, Persi, Miclo, Laurent
The purpose of this paper is to present a probabilistic proof of the well-known result stating that the time needed by a continuous-time finite birth and death process for going from the left end to...
On times to quasi-stationarity for birth and death processes (2007)
Diaconis, Persi, Miclo, Laurent
The purpose of this paper is to present a probabilistic proof of the well-known result stating that the time needed by a continuous-time finite birth and death process for going from the left end to...
Graph limits and exchangeable random graphs (2007)
Abstract. We develop a clear connection between deFinetti’s theorem for exchangeable arrays (work of Aldous–Hoover–Kallenberg) and the emerging area of graph limits (work of Lovász and many...
On times to quasi-stationarity for birth and death processes (2007)
Diaconis, Persi, Miclo, Laurent
The purpose of this paper is to present a probabilistic proof of the well-known result stating that the time needed by a continuous-time finite birth and death process for going from the left end to...
On times to quasi-stationarity for birth and death processes (2007)
Diaconis, Persi, Miclo, Laurent
The purpose of this paper is to present a probabilistic proof of the well-known result stating that the time needed by a continuous-time finite birth and death process for going from the left end to...
Sun, Jun, Boyd, Stephen, Xiao, Lin, Diaconis, Persi
We consider a Markov process on a connected graph, with edges labeled with transition rates between the adjacent vertices. The distribution of the Markov process converges to the uniform distribution...
Separation cut-offs for birth and death chains (2006)
Diaconis, Persi, Saloff-Coste, Laurent
This paper gives a necessary and sufficient condition for a sequence of birth and death chains to converge abruptly to stationarity, that is, to present a cut-off. The condition involves the notions...
Supercharacter formulas for pattern groups (2006)
Diaconis, Persi, Thiem, Nathaniel
C. Andre and N. Yan introduced the idea of a supercharacter theory to give a tractable substitute for character theory in wild groups such as the unipotent uppertriangular group $U_n(F_q)$. In this...
Bayesian analysis for reversible Markov chains (2006)
Diaconis, Persi, Rolles, Silke W. W.
We introduce a natural conjugate prior for the transition matrix of a reversible Markov chain. This allows estimation and testing. The prior arises from random walk with reinforcement in the same way...
Bayesian analysis for reversible Markov chains (2006)
Diaconis, Persi, Rolles, Silke W. W.
We introduce a natural conjugate prior for the transition matrix of a reversible Markov chain. This allows estimation and testing. The prior arises from random walk with reinforcement in the same way...
Fastest mixing Markov chain on a path (2006)
Stephen Boyd, Persi Diaconis, Jun Sun, Lin Xiao
Simulation using Markov chain Monte Carlo is a mainstay of scientific computing; see, e.g., [4, 5] for pointers to the literature. Thus the analysis and design of fast mixing Markov PSfrag chains,...
Jun Sun, Stephen Boyd, Lin Xiao, Persi Diaconis
Abstract. We consider a Markov process on a connected graph, with edges labeled with transition rates between the adjacent vertices. The distribution of the Markov process converges to the uniform...
Fastest mixing Markov chain on a path (2006)
Stephen Boyd, Persi Diaconis, Jun Sun, Lin Xiao
We consider the problem of assigning transition probabilities to the edges of a path, so the resulting Markov chain or random walk mixes as rapidly as possible. In this note we prove that fastest...
Fastest mixing Markov chain on a path (2006)
Stephen Boyd, Persi Diaconis, Jun Sun, Lin Xiao
Simulation using Markov chain Monte Carlo is a mainstay of scientific computing; see, e.g., [4, 5] for pointers to the literature. Thus the analysis and design of fast mixing Markov PSfrag chains,...
Joseph Blitzstein, Persi Diaconis
Random graphs with a given degree sequence are a useful model capturing several features absent in the classical Erdős-Rényi model, such as dependent edges and non-binomial degrees. In this paper,...
Symmetry Analysis of Reversible Markov Chains (2005)
Boyd, Stephen, Diaconis, Persi, Parrilo, Pablo, Xiao, Lin
We show how to use subgroups of the symmetry group of a reversible Markov chain to give useful bounds on eigenvalues and their multiplicity. We supplement classical representation theoretic tools...
Exchangeable pairs and Poisson approximation (2005)
Chatterjee, Sourav, Diaconis, Persi, Meckes, Elizabeth
This is a survey paper on Poisson approximation using Stein’s method of exchangeable pairs. We illustrate using Poisson-binomial trials and many variations on three classical problems of...
Symmetry analysis of reversible markov chains (2005)
Stephen Boyd, Persi Diaconis, Pablo Parrilo, Lin Xiao
We show how to use subgroups of the symmetry group of a reversible Markov chain to give useful bounds on eigenvalues and their multiplicity. We supplement classical representation theoretic tools...
Symmetry analysis of reversible markov chains (2005)
Stephen Boyd, Persi Diaconis, Pablo Parrilo, Lin Xiao
Abstract. We show how to use subgroups of the symmetry group of a reversible Markov chain to give useful bounds on eigenvalues and their multiplicity. We supplement classical representation theoretic...
Sequential Monte Carlo methods for statistical analysis of tables (2005)
Yuguo Chen, Persi Diaconis, Susan P. Holmes, Jun S. Liu
We describe a sequential importance sampling (SIS) procedure for analyzing two-way zero-one or contingency tables with fixed marginal sums. An essential feature of the new method is that it samples...
Symmetry analysis of reversible markov chains (2005)
Stephen Boyd, Persi Diaconis, Pablo Parrilo, Lin Xiao
We show how to use subgroups of the symmetry group of a reversible Markov chain to give useful bounds on eigenvalues and their multiplicity. We supplement classical representation theoretic tools...
Exchangeable pairs and Poisson approximation (2004)
Chatterjee, Sourav, Diaconis, Persi, Meckes, Elizabeth
This is a survey paper on Poisson approximation using Stein's method of exchangeable pairs. We illustrate using Poisson-binomial trials and many variations on three classical problems of...
Markov bases for noncommutative Fourier analysis of ranked data (2004)
Diaconis, Persi, Eriksson, Nicholas
To calibrate Fourier analysis of $S_5$ ranking data by Markov chain Monte Carlo techniques, a set of moves (Markov basis) is needed. We calculate this basis, and use it to provide a new statistical...
Analysis of systematic scan Metropolis algorithms using Iwahori-Hecke algebra techniques (2004)
Analysis of systematic scan Metropolis algorithms using Iwahori-Hecke algebra techniques
Diaconis, Persi, Mayer-Wolf, Eddy, Zeitouni, Ofer, Zerner, Martin P. W.
We consider a Markov chain on the space of (countable) partitions of the interval $[0,1]$, obtained first by size-biased sampling twice (allowing repetitions) and then merging the parts (if the...
Numerical Results for the Metropolis Algorithm (2004)
Diaconis, Persi, Neuberger, J. W.
This paper deals with the spectrum of an operator associated with a special kind of random walk. The operator is related to the Metropolis algorithm, an important tool of large-scale scientific...
Dynamical bias in the coin toss (2004)
Persi Diaconis, Susan Holmes, Richard Montgomery
We analyze the natural process of flipping a coin which is caught in the hand. We prove that vigorously-flipped coins are biased to come up the same way they started. The amount of bias depends on a...
Fastest mixing Markov chain on a graph (2004)
Stephen Boyd, Persi Diaconis, Lin Xiao
Author names in alphabetical order. Submitted to SIAM Review, problems and techniques section. We consider a symmetric random walk on a connected graph, where each edge is labeled with the...
Persi Diaconis, Eddy Mayer-wolf, Ofer Zeitouni, Martin P. W. Zerner, A Us-israel Bsf Grant
transformations
Jun Sun, Stephen Boyd, Lin Xiao, Persi Diaconis
We consider a Markov process on a connected graph, with edges labeled with transition rates between the adjacent vertices. The distribution of the Markov process converges to the uniform distribution...
Solitaire: Man versus machine (2004)
Xiang Yan, Persi Diaconis, Paat Rusmevichientong, Benjamin Van Roy
In this paper, we use the rollout method for policy improvement to analyze a version of Klondike solitaire. This version, sometimes called thoughtful solitaire, has all cards revealed to the player,...
Fastest mixing Markov chain on a graph (2004)
Stephen Boyd, Persi Diaconis, Lin Xiao
Author names in alphabetical order.
Persi Diaconis, Eddy Mayer-wolf, Ofer Zeitouni, Martin P. W. Zerner
Dedicated to the memory of Bob Brooks (1952–2002) We consider a Markov chain on the space of (countable) partitions of the interval [0, 1], obtained first by size-biased sampling twice (allowing...
Solitaire: Man versus machine (2004)
Xiang Yan, Persi Diaconis, Paat Rusmevichientong, Benjamin Van Roy
In this paper, we use the rollout method for policy improvement to analyze a version of Klondike solitaire. This version, sometimes called thoughtful solitaire, has all cards revealed to the player,...
Diaconis, Persi, Mayer-Wolf, Eddy, Zeitouni, Ofer, Zerner, Martin
We consider a Markov chain on the space of (countable) partitions of the interval [0,1], obtained first by size biased sampling twice (allowing repetitions) and then merging the parts (if the sampled...
Spearman's Footrule as a Measure of Disarray. (2002)
Spearman's rho and Kendall tau are related to two less widely used measures of association: Spearman's footrule and the minimum number of transitions. The means, variances, and limiting normality of...
On the Distribution of the Greatest Common Divisor. (2002)
The limiting joint distribution of the least common multiple and the greatest common divisor is determined. The lead term is given for the moments of both marginal distributions. The results are...
The Analysis of Sequential Experiments with Feedback to Subjects. (2002)
A problem arising in taste testing, medical, and parapsychology experiments can be modeled as follows. A deck of n cards contains c(i) cards labeled i, 1 < or = i < or = r. A subject guesses at the...
Factoring Probabilities on Compact Groups. (2002)
Diaconis,Persi, Shashahani,Mehrdad
When can a probability P be factored as P1 * P2? This problem arises in efficient generation of pseudo random integers and permutations. It is thus natural to think of P defined on a group. We show...
Variables on Scatterplots Look More Highly Correlated When the Scales are Increased. (2002)
Cleveland,William S., Diaconis,Persi, McGill,Robert
Subjects were shown scatterplots and were asked to judge the amount of association between the two variables. Judged association increased when the scales on the horizontal and vertical axes were...
Unitary Correlations and the Fejer Kernel (2002)
Daniel Bump, Persi Diaconis, Joseph B. Keller
Abstract. Let M be a unitary matrix with eigenvalues t j, and let f be a function on the unit circle. Define X f (M) = P f(t j). We derive exact and asymptotic formulae for the covariance of X f and...
A different construction of Gaussian fields from Markov chains: Dirichlet covariances (2002)
Persi Diaconis, Steven, N. Evans
Abstract. We study a class of Gaussian random fields with negative correlations. These fields are easy to simulate. They are defined in a natural way from a Markov chain that has the index space of...
A different construction of Gaussian fields from Markov chains: Dirichlet covariances (2002)
Persi Diaconis, Steven, N. Evans
Abstract. We study a class of Gaussian random elds with negative correlations. These elds are easy to simulate. They are de ned in a natural way from a Markov chain that has the index space of the...
Unitary Correlations and the Fejér Kernel (2002)
Daniel Bump, Persi Diaconis, Joseph B. Keller
Let M be a unitary matrix with eigenvalues t j , and let f be a function on the unit circle. Define X f (M) = f(t j ). We derive exact and asymptotic formulae for the covariance of X f and X g with...
A Geometric Interpretation of the Metropolis-Hastings Algorithm (2001)
Billera, Louis J., Diaconis, Persi
The Metropolis–Hastings algorithm transforms a given stochastic matrix into a reversible stochastic matrix with a prescribed stationary distribution. We show that this transformation gives the...
The Asymmetric One-Dimensional Constrained Ising Model (2001)
Aldous, David, Diaconis, Persi
We study a reversible one-dimensional spin system with Bernoulli(p) stationary distribution, in which a site can flip only if the site to its left is in state +1. Such models have been used as simple...
Linear functionals of eigenvalues of random matrices (2001)
Persi Diaconis, Steven, N. Evans
Abstract. Let Mn be a random n × n unitary matrix with distribution given by Haar measure on the unitary group. Using explicit moment calculations, a general criterion is given for linear...
Linear functionals of eigenvalues of random matrices (2001)
Persi Diaconis, Steven, N. Evans
Abstract. Let Mn be a random n n unitary matrix with distribution given by Haar measure on the unitary group. Using explicit moment calculations, a general criterion is given for linear combinations...
G.H. Hardy and Probability???? (2001)
Despite a true antipathy to the subject Hardy contributed deeply to modern probability. His work with Ramanujan begat probabilistic number theory. His work on Tauberian theorems and divergent series...
Analysis of a nonreversible Markov chain sampler (2000)
Diaconis, Persi, Holmes, Susan, Neal, Radford M.
We analyze the convergence to stationarity of a simple nonreversible Markov chain that serves as a model for several nonreversible Markov chain sampling methods that are used in practice. Our...
Analysis of systematic scan Metropolis algorithms using Iwahori-Hecke algebra techniques (2000)
. We give the rst analysis of a systematic scan version of the Metropolis algorithm. Our examples include generating random elements of a Coxeter group with probability determined by the length...
Immanants And Finite Point Processes (2000)
Persi Diaconis, Steven, STEVEN N. EVANS, In This Case
. Given a Hermitian, non-negative definite kernel K and a character of the symmetric group on n letters, define the corresponding immanant function K [x 1 ; : : : ; xn ] := P oe (oe) Q n i=1 K(x i ;...
Linear Functionals Of Eigenvalues Of Random Matrices (2000)
Persi Diaconis, Steven, Steven N. Evans
. Let Mn be a random n \Theta n unitary matrix with distribution given by Haar measure on the unitary group. Using explicit moment calculations, a general criterion is given for linear combinations...
Immanants and finite point processes (2000)
Persi Diaconis, Steven, N. Evans
Abstract. Given a Hermitian, non-negative de nite kernel K and a character of the symmetric group on n letters, de ne the corresponding immanant function K [x1;:::;xn]: = P ( ) Qn i=1 K(xi;x (i)),...
Statistical problems involving permutations with restricted positions (1999)
Persi Diaconis, Ronald Graham, Susan P. Holmes
The rich world of permutation tests can be supplemented by a variety of applications where only some permutations are permitted. We consider two examples: testing independence with truncated data and...
Longest Increasing Subsequences: From Patience Sorting to the Baik-Deift-Johansson Theorem (1999)
We describe a simple one-person card game, patience sorting. Its analysis leads to a broad circle of ideas linking Young tableaux with the longest increasing subsequence of a random permutation via...
Iterated random functions (1999)
Persi Diaconis, David Freedman
Abstract. Iterated random functions are used to draw pictures or simulate large Ising models, among other applications. They offer a method for studying the steady state distribution of a Markov...
Iterated random functions (1999)
Persi Diaconis, David Freedman
Abstract. Iterated random functions are used to draw pictures or simulate large Ising models, among other applications. They offer a method for studying the steady state distribution of a Markov...
Exact Rates of Convergence for Some Simple Non-Reversible Markov Chains (1999)
Elizabeth Lee Wilmer, Elizabeth Lee Wilmer, Persi Diaconis
We describe the behavior of certain families of Markov chains as they approach their stationary distributions. Prior methods do not work well for these chains, which are non-reversible, have...
Longest increasing subsequences: from patience sorting to the Baik-Deift-Johansson theorem (1999)
Abstract. We describe a simple one-person card game, patience sorting. Its analysis leads to a broad circle of ideas linking Young tableaux with the longest increasing subsequence of a random...
A Note on Non-Linear Functions of Linear Combinations. (1998)
Diaconis,Persi, Shashahani,Mehrdad
Projection pursuit algorithms approximate a function of p variables by a sum of non-linear functions of linear combinations. We develop some approximation theory, give a necessary and sufficient...
Updating Subjective Probability. (1998)
Diaconis,Persi, Zabell,Sandy L.
This paper discusses some of the mathematical properties of Jeffrey's rule for revising a probability P to a new probability P*, connecting it with sufficient partitions, and maximum entropy updating...
Projection Pursuit Regression: Some Mathematics. (1998)
Diaconis,Persi, Shahshahani,Mehrdad
We present some mathematical analysis for a class of curve fitting algorithms labeled 'projection pursuit' algorithms. These algorithms approximate a general function of p variables by a sum of...
Random walks and hyperplane arrangements (1998)
Brown, Kenneth S., Diaconis, Persi
Let $\mathscr{C}$ be the set of chambers of a real hyperplane arrangement. We study a random walk on $\mathscr{C}$ introduced by Bidigare, Hanlon and Rockmore. This includes various shuffling schemes...
Algebraic algorithms for sampling from conditional distributions (1998)
Diaconis, Persi, Sturmfels, Bernd
We construct Markov chain algorithms for sampling from discrete exponential families conditional on a sufficient statistic. Examples include contingency tables, logistic regression, and spectral...
Algebraic algorithms for sampling from conditional distributions (1998)
Persi Diaconis, Bernd Sturmfels
We construct Markov chain algorithms for sampling from discrete exponential families conditional on a sufficient statistic. Examples include generating tables with fixed row and column sums and...
Analysis of a Non-Reversible Markov Chain Sampler (1997)
Persi Diaconis, Susan Holmes, Radford M. Neal
We analyse the convergence to stationarity of a simple non-reversible Markov chain that serves as a model for several non-reversible Markov chain sampling methods that are used in practice. Our...
Hammersley's Interacting Particle Process and Longest Increasing Subsequences (1995)
In a famous paper [8] Hammersley investigated the length Ln of the longest increasing subsequence of a random n-permutation. Implicit in that paper is a certain one-dimensional continuous-space...
Efficient Computation of Isotypic Projections for the Symmetric Group (1993)
Persi Diaconis, Daniel Rockmore
. Spectral analysis on the symmetric group Sn calls for computing projections of functions defined on Sn and its homogeneous spaces, onto invariant subspaces. In particular, for the analysis of...
An affine walk on the hypercube (1992)
Diaconis, P. and R. Graham, An affine walk on the hypercube, Journal of Computational and Applied Mathematics 41 (1992) 215-235. Let Z $ be the group of binary d-tuples. We study the process X,, =...
North-Holland Universal structures (1991)
Fan Chung, Persi Diaconis, Ron Graham, P. Diaconis, R. Graham
North-Holland Universal structures (1991)
Fan Chung, Persi Diaconis, Ron Graham, P. Diaconis, R. Graham
Weak and strong averages in probability and the theory of numbers.
Thesis (Ph. D.)--Harvard University, 1974.
Random Walks And Plane Arrangements In Three Dimensions
Louis J. Billera, Kenneth S. Brown, Persi Diaconis
. This paper explains some modern geometry and probability in the course of solving a random walk problem. Consider n planes through the origin in three dimensional Euclidean space. Assume, for...
Random Walk And Hyperplane Arrangements
Kenneth S. Brown, Persi Diaconis
. Let C be the set of chambers of a real hyperplane arrangement. We study a random walk on C introduced by Bidigare, Hanlon, and Rockmore. This includes various shuffling schemes used in computer...
Supercharacter formulas for pattern groups
C. Andre and N. Yan introduced the idea of a supercharacter theory to give a tractable substitute for character theory in wild groups such as the unipotent uppertriangular group $U_n(mathbb {F}_q...