Concentration inequalities for Gibbs measures. (English) Zbl 1233.60010
The author considers log-Sobolev inequalities and their relationship with concentration properties on high dimensional spaces, namely, unbounded spin systems on the \(d\)-dimensional lattice with interactions that increase slower than quadratic are investigated. Assuming that the one-site measure satisfies a modified log-Sobolev inequality with a constant uniformly on the boundary conditions, the conditions are determined so that the infinite-dimensional Gibbs measure satisfies a concentration and a Talagrand type inequality. Also, a modified log-Sobolev type concentration property is obtained under weaker conditions referring to the log-Sobolev inequalities for the boundary free measure.
Reviewer: Vygantas Paulauskas (Vilnius)
MSC:
| 60E15 | Inequalities; stochastic orderings |
| 26D10 | Inequalities involving derivatives and differential and integral operators |
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