A NOTE ON SPECTRAL GAP AND WEIGHTED POINCARE INEQUALITIES FOR SOME ONE-DIMENSIONAL DIFFUSIONS

作者：Bonnefont, Michel^*; Joulin, Alderic; Ma, Yutao

来源：ESAIM: Probability and Statistics , 2016, 20: 18-29.

DOI：10.1051/ps/2015019

• Spectral gap
• diffusion operator
• weighted Poincare inequality

We present some classical and weighted Poincare 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 Poincare 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.

• 出版日期2016
• 单位北京师范大学