Concentration bounds for geometric Poisson functionals: logarithmic Sobolev inequalities revisited

DOI10.1214/16-EJP4235zbMath1337.60011arXiv1504.03138MaRDI QIDQ287689

Giovanni Peccati, Sascha Bachmann

Publication date: 23 May 2016

Published in: Electronic Journal of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1504.03138

zbMATH Keywords

Poisson measurerandom graphsstochastic geometrylogarithmic Sobolev inequalitiesconcentration of measureconvex distanceHerbst argument

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Combinatorial probability (60C05) Random measures (60G57)

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Concentration for Poisson functionals: component counts in random geometric graphs ⋮ Concentration for Poisson \(U\)-statistics: subgraph counts in random geometric graphs ⋮ The fourth moment theorem on the Poisson space ⋮ The Malliavin–Stein Method on the Poisson Space ⋮ Concentration inequalities for Poisson point processes with application to adaptive intensity estimation ⋮ Upper large deviations for power-weighted edge lengths in spatial random networks ⋮ A modified \(\Phi \)-Sobolev inequality for canonical Lévy processes and its applications ⋮ Restricted hypercontractivity on the Poisson space ⋮ Multiscale functional inequalities in probability: constructive approach ⋮ A concentration inequality for inhomogeneous Neyman-Scott point processes ⋮ Concentration on Poisson spaces via modified \(\Phi\)-Sobolev inequalities ⋮ Transport inequalities for random point measures ⋮ Concentration inequalities for measures of a Boolean model ⋮ Modified log-Sobolev inequalities, Beckner inequalities and moment estimates ⋮ Limit theory for the Gilbert graph

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