BONNEFONT, Michel; JOULIN, Aldéric; MA, Yutao

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BONNEFONT, Michel
Institut de Mathématiques de Bordeaux [IMB]

JOULIN, Aldéric
Institut de Mathématiques de Toulouse UMR5219 [IMT]

MA, Yutao
Beijing Normal University [BNU]

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Article de revue

Ce document a été publié dans

ESAIM: Probability and Statistics. 2016-06-03, vol. 20

EDP Sciences

Résumé en anglais

We present some classical and weighted Poincar\'e inequalities for some one-dimensional probability measures. This work is the one-dimensional counterpart of a recent study achieved by the authors for a class of spherically symmetric probability measures in dimension larger than 2. Our strategy is based on two main ingredients: on the one hand, the optimal constant in the desired weighted Poincar\'e inequality has to be rewritten as the spectral gap of a convenient Markovian diffusion operator, and on the other hand we use a recent result given by the two first authors, which allows to estimate precisely this spectral gap. In particular we are able to capture its exact value for some examples.< Réduire

URI

https://oskar-bordeaux.fr/handle/20.500.12278/194571

Project ANR

Aux frontières de l'analyse Harmonique - ANR-12-BS01-0013
Stabilité du comportement asymptotique d'EDP, de processus stochastiques et de leurs discrétisations. - ANR-12-BS01-0019
Géométrie des mesures convexes et discrètes - ANR-11-BS01-0007

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Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251