Convex concentration inequalities for continuous gas and stochastic domination

In this article, we consider the continuous gas in a bounded domain Λ of ℝ+ or ℝd described by a Gibbsian probability measure μηΛ associated with a pair interaction ϕ, the inverse temperature β, the activity z > 0, and the boundary condition η. Define F = ∫ f(s)ωΛ(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 μηΛ. 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.