关键词: continuous gas, Gibbs measure, convex concentration inequality, Itos formula, stochastic domination

Abstract:

In this article,  we consider the continuous gas in a bounded domain ∧of R⁺ or R^d described by a Gibbsian probability measure
μ^η_∧ associated with a pair interaction Φ, the inverse temperature β, the activity z>0, and the boundary condition η. Define F=∫f(s)ω∧(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 μ^η_∧. 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.

Key words: continuous gas, Gibbs measure, convex concentration inequality, Itos formula, stochastic domination