A group of us in Nice, have recently had a very useful interaction across fields. The fields are, one the one hand, hard analysis (micro-local techniques, functional inequalities of Nash and log-sobolev type) and on the other hand, rates of convergence of Markov chains to their stationary distributions (how many times to shuffle cards?).

We would like to broaden and continue this dialog through a conference in Nice June 15-19, 2009.The conference will be small (weexpect 20+) with expository talks aimed at teaching the problems and techniques of 'one side' to the 'other' and real oportunities for interacting.

Of course, the interactions between probability and analysis are classical and widespread, so we want to try and focus the conference around the theme of quantitative bounds on large time behavior (equivalently, rates of convergence for Markov chains), being liberal about interpertation.