CONVEX CONCENTRATION INEQUALITIES FOR CONTINUOUS GAS AND STOCHASTIC DOMINATION

In this article, we consider the continuous gas in a bounded domain A of R+ or R-d described by a Gibbsian probability measure mu(eta)(Lambda) associated with a pair interaction phi, the inverse temperature beta, the activity z > 0, and the boundary condition eta. Define F = integral f(s)omega(Lambda) (ds). Applying the generalized Ito's formula for forward-backward martingales (see Klein et al. [5]), we obtain convex concentration inequalities for F with respect to the Gibbs measure mu(eta)(Lambda). On the other hand, by FKG inequality on the Poisson space, we also give a new simple argument for the stochastic domination for the Gibbs measure.