Transport inequalities for random point measures

We derive transport-entropy inequalities for mixed binomial point processes, and Poisson processes. show that when the finite intensity measure satisfies a Talagrand transport inequality, law of process also type inequality. (with arbitrary ?-finite measure) always universal inequality à la Marton. explore consequences these in terms concentration modified logarithmic Sobolev inequalities. In particular, our results allow one to extend deviation by Reitzner [33], originally proved random measures with mass.