Let $\delta_c(X)$ denote the maximum $d$ in $\lbrack 0, \frac{1}{2}\rbrack$ such that a binary Gibbs random field $X$ can be decomposed as the modulo 2 sum of two independent binary fields, one of which is independent Bernoulli (white binary noise) of weight $d$. In a recent paper, Hajek and Berger showed, under modest assumptions, that $\delta_c > 0$. We point out here that the decomposition of $X$ is related to the classic statistical mechanics problem of determining zero-free regions of partition functions. A theorem of Ruelle is then applied to obtain improved estimates for $\delta_c$.
Publié le : 1987-07-14
Classification:
Decomposition,
random fields,
Gibbs distributions,
partition functions,
zeros,
distortion theory,
60G60,
94A34,
60B15,
82A05
@article{1176992085,
author = {Newman, Charles M.},
title = {Decomposition of Binary Random Fields and Zeros of Partition Functions},
journal = {Ann. Probab.},
volume = {15},
number = {4},
year = {1987},
pages = { 1126-1130},
language = {en},
url = {http://dml.mathdoc.fr/item/1176992085}
}
Newman, Charles M. Decomposition of Binary Random Fields and Zeros of Partition Functions. Ann. Probab., Tome 15 (1987) no. 4, pp. 1126-1130. http://gdmltest.u-ga.fr/item/1176992085/