A note on spectral gap and weighted Poincaré inequalities for some one-dimensional diffusions

Michel Bonnefont; Aldéric Joulin; Yutao Ma

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arXiv · 1411.5982

A note on spectral gap and weighted Poincaré inequalities for some one-dimensional diffusions

Michel Bonnefont·Aldéric Joulin·Yutao Ma

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Abstract

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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Michel Bonnefont, Aldéric Joulin, Yutao Ma. 2014-11-21. A note on spectral gap and weighted Poincaré inequalities for some one-dimensional diffusions. https://arxiv.org/abs/1411.5982

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