We study translation-invariant random-cluster measures with
techniques from large deviation theory and convex analysis. In particular, we
prove a large deviation principle with rate function given by a specific
entropy, and a Dobrushin-Lanford-Ruelle variational principle that
characterizes translation-invariant random-cluster measures as the solutions of
the variational equation for free energy. Consequences of these theorems
include inequalities for edge and cluster densities of translation-invariant
random-cluster measures.
Publié le : 1998-07-14
Classification:
Relative entropy,
variational principle,
large deviations,
random-cluster measure,
60K35,
60F10,
82B20,
82B43
@article{1022855747,
author = {Sepp\"al\"ainen, Timo},
title = {Entropy for translation-invariant random-cluster
measures},
journal = {Ann. Probab.},
volume = {26},
number = {1},
year = {1998},
pages = { 1139-1178},
language = {en},
url = {http://dml.mathdoc.fr/item/1022855747}
}
Seppäläinen, Timo. Entropy for translation-invariant random-cluster
measures. Ann. Probab., Tome 26 (1998) no. 1, pp. 1139-1178. http://gdmltest.u-ga.fr/item/1022855747/