论文标题
随机点措施的运输不平等
Transport inequalities for random point measures
论文作者
论文摘要
我们得出了混合二项点过程和泊松点过程的转运 - 凝集不平等。我们表明，当有限的强度措施满足Talagrand运输不平等时，该积分过程的定律也满足了Talagrand类型的运输不平等。我们还表明，泊松点过程（具有任意$σ$ -Finite强度度量）始终满足通用的运输 - 内向不平等。我们探讨了这些不平等的后果，从度量的浓度和修改的对数Sobolev不平等方面探讨了这些不平等。特别是，我们的结果使人们可以扩大Reitzner [31]的偏差不平等，最初证明是有限质量的泊松随机度量。
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 [31], originally proved for Poisson random measures with finite mass.
