By Gilles Royer

This e-book presents an creation to logarithmic Sobolev inequalities with a few vital functions to mathematical statistical physics. Royer starts off by way of amassing and reviewing the required heritage fabric on selfadjoint operators, semigroups, Kolmogorov diffusion approaches, strategies of stochastic differential equations, and sure different comparable themes. There then is a bankruptcy on log Sobolev inequalities with an software to a robust ergodicity theorem for Kolmogorov diffusion procedures. the rest chapters think of the final environment for Gibbs measures together with life and forte concerns, the Ising version with actual spins and the appliance of log Sobolev inequalities to teach the stabilization of the Glauber-Langevin dynamic stochastic types for the Ising version with actual spins. The workouts and enhances expand the cloth in general textual content to similar components akin to Markov chains. Titles during this sequence are co-published with Société Mathématique de France. SMF contributors are entitled to AMS member savings.

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