The log-Sobolev inequality for spin systems of higher order interactions

Autor:	Konstantopoulos, Takis, Papageorgiou, Ioannis
Rok vydání:	2019
Předmět:	Mathematics - Probability Mathematical Physics Mathematics - Functional Analysis 60K35 26D10 39B62 22E30
Druh dokumentu:	Working Paper
Popis:	We study the infinite-dimensional log-Sobolev inequality for spin systems on $\mathbb{Z}^d$ with interactions of power higher than quadratic. We assume that the one site measure without a boundary $e^{-\phi(x)}dx/Z$ satisfies a log-Sobolev inequality and we determine conditions so that the infinite-dimensional Gibbs measure also satisfies the inequality. As a concrete application, we prove that a certain class of nontrivial Gibbs measures with non-quadratic interaction potentials on an infinite product of Heisenberg groups satisfy the log-Sobolev inequality.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1906.11980 Zobrazit plný text záznamu View this record from Arxiv