The Logarithmic Sobolev Inequality in Infinite Dimensions for Unbounded Spin Systems on the Lattice with Non-Quadratic Interactions

I. Papageorgiou

2010, v.16, Issue 3, 447-484

ABSTRACT

We are interested in the Logarithmic Sobolev inequality for the infinite volume Gibbs measure with no quadratic interactions. We consider unbounded spin systems on the one-dimensional lattice with interactions that go beyond the usual strict convexity and without uniform bound on the second derivative. We assume that the one-dimensional single-site measure with boundaries satisfies the Log-Sobolev inequality uniformly in the boundary conditions and we determine conditions under which the Log-Sobolev inequality can be extended to the infinite volume Gibbs measure.

Keywords: Logarithmic Sobolev inequality,Gibbs measure,infinitedimensions,spin systems