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