Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6415061 | Journal of Functional Analysis | 2016 | 27 Pages |
Abstract
Let μ be a probability measure on Rn (nâ¥2) with Lebesgue density proportional to eâV(âxâ), where V:R+âR is a smooth convex potential. We show that the associated spectral gap in L2(μ) lies between (nâ1)/â«Rnâxâ2μ(dx) and n/â«Rnâxâ2μ(dx), improving a well-known two-sided estimate due to Bobkov. Our Markovian approach is remarkably simple and is sufficiently robust to be extended beyond the log-concave case, at the price of potentially modifying the underlying operator in the energy, leading to weighted Poincaré inequalities. All our results are illustrated by some classical and less classical examples.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Michel Bonnefont, Aldéric Joulin, Yutao Ma,