Transport inequalities for random point measures

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 tha...

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Veröffentlicht in:Journal of functional analysis 2021-11, Vol.281 (9), p.109141, Article 109141
Hauptverfasser: Gozlan, Nathaël, Herry, Ronan, Peccati, Giovanni
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2021.109141