A note on spectral gap and weighted Poincar\'e inequalities for some one-dimensional diffusions
Probability
2014-11-24 v1
Abstract
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.
Cite
@article{arxiv.1411.5982,
title = {A note on spectral gap and weighted Poincar\'e inequalities for some one-dimensional diffusions},
author = {Michel Bonnefont and Aldéric Joulin and Yutao Ma},
journal= {arXiv preprint arXiv:1411.5982},
year = {2014}
}