Concentration inequalities for Gibbs measures

Details Concentration inequalities for Gibbs measures Concentration inequalities for Gibbs measures

2010-04-20

arxiv.org/abs/1004.3482v4

Mathematics

Probability

28 pages, accepted for publication at Infinite Dimensional Analysis, Quantum Probability and Related Topics

Scientific paper

We are interested in Sobolev type inequalities and their relationship with concentration properties on higher dimensions. We consider unbounded spin systems on the d-dimensional lattice with interactions that increase slower than a quadratic. At first we assume that the one site measure satisfies a Modified log-Sobolev inequality with a constant uniformly on the boundary conditions and we determine conditions so that the infinite dimensional Gibbs measure satisfies a concentration as well as a Talagrand type inequality. Then a Modified Log-Sobolev type concentration property is obtained under weaker conditions referring to the Log-Sobolev inequalities for the boundary free measure.

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