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

我们推导出混合二项式点过程和泊松点过程的传输熵不等式。我们表明，当有限强度测度满足 Talagrand 输运不等式时，点过程定律也满足 Talagrand 型输运不等式。我们还表明泊松点过程（具有任意的σ -有限强度度量）总是满足马顿的普遍传输熵不等式。我们探讨了这些不等式在度量集中和修正对数 Sobolev 不等式方面的后果。特别是，我们的结果允许扩展 Reitzner [33] 的偏差不等式，最初证明了具有有限质量的泊松随机测度。