A note on spectral gap and weighted Poincaré inequalities for some one-dimensional diffusions
We present some classical and weighted Poincaré 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 bas...
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Published in | Probability and statistics Vol. 20; pp. 18 - 29 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Les Ulis
EDP Sciences
2016
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Subjects | |
Online Access | Get full text |
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Summary: | We present some classical and weighted Poincaré 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 Poincaré 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. |
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Bibliography: | MB is partially supported by the French ANR-12-BS01-0013-02 HAB project. ark:/67375/80W-XXX64Q82-0 publisher-ID:ps150019 PII:S1292810015000191 istex:37F88CE44E0AD3BF3C48D2DAEE9DDFA83D3D14F6 |
ISSN: | 1292-8100 1262-3318 |
DOI: | 10.1051/ps/2015019 |