The Logarithmic Sobolev Inequality for Gibbs Measures on Infinite Product of Heisenberg Groups

I. Papageorgiou

2014, v.20, Issue 4, 705-749

ABSTRACT

We are interested in the q logarithmic Sobolev inequality for the infinite dimensional Gibbs measure on the lattice. In particular we focus on measures on the infinite product of Heisenberg groups. We assume that the one site boundary free measure satisfies either a q log-Sobolev inequality or a U-Bound inequality, and we determine conditions so that the infinite dimensional Gibbs measure satisfies a $q$ log-Sobolev inequality.

Keywords: log-Sobolev inequality,Heisenberg group,Gibbs measure

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Laboratory of large random systems, Dept. of Mechanics and Mathematics
Moscow State University, Vorobievy Gory, 119952 Moscow Russia
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The journal was founded in 1995 by prof. Malyshev V. A.
Published by Polymat Publishing Company, Moscow, Russia
ISSN 1024-2953
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I. Papageorgiou