Consider a binary Markov random field whose neighbor structure is specified by a countable graph with nodes of uniformly bounded degree. Under a minimal assumption we prove a decomposition theorem to the effect that such a Markov random field can be represented as the nodewise modulo 2 sum of two independent binary random fields, one of which is white binary noise of positive weight. Said decomposition provides the information theorist with an exact expression for the per-site rate-distortion function of the random field over an interval of distortions not exceeding this weight. We mention possible implications for communication theory, probability theory and statistical physics.
Publié le : 1987-07-14
Classification:
Markov random field,
Gibbs random field,
Ising model,
rate-distortion function,
60G60,
94A34,
60K35
@article{1176992084,
author = {Hajek, Bruce and Berger, Toby},
title = {A Decomposition Theorem for Binary Markov Random Fields},
journal = {Ann. Probab.},
volume = {15},
number = {4},
year = {1987},
pages = { 1112-1125},
language = {en},
url = {http://dml.mathdoc.fr/item/1176992084}
}
Hajek, Bruce; Berger, Toby. A Decomposition Theorem for Binary Markov Random Fields. Ann. Probab., Tome 15 (1987) no. 4, pp. 1112-1125. http://gdmltest.u-ga.fr/item/1176992084/