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arXiv · 1004.3482

Concentration inequalities for Gibbs measures

Ioannis Papageorgiou
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Abstract

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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Ioannis Papageorgiou. 2010-04-20. Concentration inequalities for Gibbs measures. https://doi.org/10.1142/s0219025711004316

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