Propp–Wilson Algorithms and Finitary Codings for High Noise Markov Random Fields

In this paper, we combine two previous works, the first being by the first author and K. Nelander, and the second by J. van den Berg and the second author, to show (1) that one can carry out a Propp–Wilson exact simulation for all Markov random fields on Zd satisfying a certain high noise assumption, and (2) that all such random fields are a finitary image of a finite state i.i.d. process. (2) is a strengthening of the previously known fact that such random fields are so-called Bernoulli shifts.

[1]  P. Green,et al.  Exact Sampling from a Continuous State Space , 1998 .

[2]  O. Haggstrom,et al.  On Exact Simulation of Markov Random Fields Using Coupling from the Past , 1999 .

[3]  J. Laurie Snell,et al.  Markov Random Fields and Their Applications , 1980 .

[4]  Jeffrey E. Steif,et al.  -Convergence to equilibrium and space—time bernoullicity for spin systems in the M < ε case , 1991, Ergodic Theory and Dynamical Systems.

[5]  The random geometry of equilibrium phases , 1999, math/9905031.

[6]  J. Møller.  Perfect simulation of conditionally specified models , 1999 .

[7]  Jeffrey E. Steif,et al.  Centrum Voor Wiskunde En Informatica on the Existence and Non-existence of Finitary Codings for a Class of Random Fields , 2022 .

[8]  P. L. Dobruschin.  The Description of a Random Field by Means of Conditional Probabilities and Conditions of Its Regularity , 1968 .

[9]  Hans-Otto Georgii,et al.  Gibbs Measures and Phase Transitions , 1988 .

[10]  F. Martinelli,et al.  Approach to equilibrium of Glauber dynamics in the one phase region , 1994 .

[11]  Robert M. Burton,et al.  Quite weak Bernoulli with exponential rate and percolation for random fields , 1995 .

[12]  Lucio Russo,et al.  Markov processes, Bernoulli schemes, and Ising model , 1973 .

[13]  David Bruce Wilson,et al.  Annotated bibliography of perfectly random sampling with Markov chains , 1997, Microsurveys in Discrete Probability.

[14]  Van den Berg,et al.  Disagreement percolation in the study of Markov fields , 1994 .

[15]  David Bruce Wilson,et al.  Exact sampling with coupled Markov chains and applications to statistical mechanics , 1996, Random Struct. Algorithms.

[16]  Charles M. Newman,et al.  Topics in Disordered Systems , 1997 .

[17]  J. Propp,et al.  Exact sampling with coupled Markov chains and applications to statistical mechanics , 1996 .