Arnaud Guillin: A probabilistic criterion for logarithmic Sobolev inequality

Abstract: The logarithmic Sobolev inequality, since its first appearance in Gross paper, has attracted a lot of attention these padt thirty years, due to its various applications: entropic decay to equilibrium, concentration of measure, hypercontractivity... We will prove here that these LSI are in fact equivalent to some Lyapunov type conditions which turns out to have a nice interpretation for the natural Markov process associated to the inequality. (Joint work with Patrick Cattiaux).