The Logarithmic Sobolev Inequality in Infinite dimensions for Unbounded Spin Systems on the Lattice with non Quadratic Interactions

Details The Logarithmic Sobolev Inequality in Infinite dimensions for Unbounded Spin Systems on the Lattice with non Quadratic Interactions The Logarithmic Sobolev Inequality in Infinite dimensions for Unbounded Spin Systems on the Lattice with non Quadratic Interactions

2009-01-10

arxiv.org/abs/0901.1403v2

Markov Processes Relat. Fields 16, 447-484 (2010)

Mathematics

Functional Analysis

37 pages. Improved version. Accepted for publication in Markov Processes and Related Fields.

Scientific paper

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 on the boundary conditions and we determine conditions under which the Log-Sobolev Inequality can be extended to the infinite volume Gibbs measure.

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