Weighted second-order Poincaré inequalities: Application to RSA models

Duerinckx, Mitia; Gloria, Antoine

Type de document :

Pré-publication ou Document de travail

Titre :

Weighted second-order Poincaré inequalities: Application to RSA models

Auteur(s) :

Duerinckx, Mitia [Auteur]
Laboratoire Jacques-Louis Lions [LJLL]
Quantitative methods for stochastic models in physics [MEPHYSTO]
Département de Mathématique [Bruxelles] [ULB]
Gloria, Antoine [Auteur]
Quantitative methods for stochastic models in physics [MEPHYSTO]

Discipline(s) HAL :

Mathématiques [math]/Probabilités [math.PR]

Résumé en anglais : [en]

Consider an ergodic stationary random field A on the ambient space R d. In a recent work we introduced the notion of weighted (first-order) functional inequalities , which extend standard functional inequalities like ...
Lire la suite >Consider an ergodic stationary random field A on the ambient space R d. In a recent work we introduced the notion of weighted (first-order) functional inequalities , which extend standard functional inequalities like spectral gap, covariance, and logarithmic Sobolev inequalities, while still ensuring strong concentration properties. We also developed a constructive approach to these weighted inequalities, proving their validity for prototypical examples like Gaussian fields with arbitrary covariance function , Voronoi and Delaunay tessellations of Poisson point sets, and random sequential adsorption (RSA) models, which do not satisfy standard functional inequalities. In the present contribution, we turn to second-order Poincaré inequalities à la Chatterjee: while first-order inequalities quantify the distance to constants for nonlinear functions X(A) in terms of their local dependence on the random field A, second-order inequalities quantify their distance to normality. For the above-mentioned examples, we prove the validity of suitable weighted second-order Poincaré inequalities. Applied to RSA models, these functional inequalities allow us to complete and improve previous results by Schreiber, Penrose, and Yukich on the jamming limit, and to propose and fully analyze a more efficient algorithm to approximate the latter.Lire moins >

Langue :

Anglais

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Fichiers

document
Accès libre
Accéder au document

WSG3_v4.pdf
Accès libre
Accéder au document

Weighted second-order Poincaré inequalities: ... BibTeX CSV Excel RIS

Fichiers

Weighted second-order Poincaré inequalities: ...

BibTeX

CSV

Excel

RIS