arXiv Analytics

Sign in

arXiv:1907.05414 [math.PR]AbstractReferencesReviewsResources

Variational principle for weakly dependent random fields

Piet Lammers, Martin Tassy

Published 2019-07-11Version 1

Using an alternative notion of entropy introduced by Datta, the max-entropy, we present a new simplified framework to study the minimizers of the specific free energy for random fields which are weakly dependent in the sense of Lewis, Pfister, and Sullivan. The framework is then applied to derive the variational principle for the loop $O(n)$ model and the Ising model in a random percolation environment in the nonmagnetic phase, and we explain how to extend the variational principle to similar models. To demonstrate the generality of the framework, we indicate how to naturally fit into it the variational principle for models with an absolutely summable interaction potential, and for the random-cluster model.

Related articles: Most relevant | Search more
arXiv:1610.08103 [math.PR] (Published 2016-10-25)
A variational principle for a non-integrable model
arXiv:1005.0483 [math.PR] (Published 2010-05-04, updated 2012-03-01)
Central limit theorems for the excursion set volumes of weakly dependent random fields
arXiv:math/0107081 [math.PR] (Published 2001-07-11)
Variational principle and almost quasilocality for some renormalized measures