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We construct Markov chain algorithms for sampling from discrete exponential families conditional on a sufticient statistic. Examples include contingency tables, logistic regression, and spectral analysis of permutation data. The algorithms involve computations in polynomial rings using Grobner bases. 1. Introduction. This paper describes new algorithms for… (More)

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- Persi Diaconis, David Freedman
- SIAM Review
- 1999

A bstract. 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 chain, and give useful bounds on rates of convergence in a variety of examples. The present paper surveys the field and presents some new examples. There is a… (More)

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 coauthors). Along the way, we translate the graph theory into more classical probability .

- Dave Bayer, Persi Diaconis
- 2008

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. Institute of… (More)

- Stephen P. Boyd, Persi Diaconis, Lin Xiao
- SIAM Review
- 2004

Author names in alphabetical order. Abstract We consider a symmetric random walk on a connected graph, where each edge is labeled with the probability of transition between the two adjacent vertices. The associated Markov chain has a uniform equilibrium distribution; the rate of convergence to this distribution, i.e., the mixing rate of the Markov chain, is… (More)

- P Diaconis
- Proceedings of the National Academy of Sciences…
- 1996

Natural mixing processes modeled by Markov chains often show a sharp cutoff in their convergence to long-time behavior. This paper presents problems where the cutoff can be proved (card shuffling, the Ehrenfests' urn). It shows that chains with polynomial growth (drunkard's walk) do not show cutoffs. The best general understanding of such cutoffs (high… (More)

- Daniel Bump, Persi Diaconis
- J. Comb. Theory, Ser. A
- 2002

We give a new proof of the strong Szegö limit theorem estimating the determinants of Toeplitz matrices using symmetric function theory. We also obtain asymptotics for Toeplitz minors. If f(t)=;. −. d n t n is a function on the unit circle T in C then D n − 1 (f) will denote the Toeplitz determinant det T n − 1 (f), where T n − 1 (f) is the n × n Toeplitz… (More)

- Fan Chung Graham, Persi Diaconis, Ronald L. Graham
- Discrete Mathematics
- 1992

- Jun Sun, Stephen P. Boyd, Lin Xiao, Persi Diaconis
- SIAM Review
- 2006

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 at a rate determined by the second smallest eigenvalue λ 2 of the Laplacian of the weighted graph. In this paper we consider the problem of assigning… (More)