Intertwinings, second-order Brascamp-Lieb inequalities and spectral estimates
Language
en
Document de travail - Pré-publication
English Abstract
We explore the consequences of the so-called intertwinings between gradients and Markov diffusion operators on $R^d$ in terms of second-order Brascamp-Lieb inequalities for log-concave distributions and beyond, extending ...Read more >
We explore the consequences of the so-called intertwinings between gradients and Markov diffusion operators on $R^d$ in terms of second-order Brascamp-Lieb inequalities for log-concave distributions and beyond, extending our inequalities established in a previous paper. As a result, we derive some convenient lower bounds on the $(d+1)^{th}$ positive eigenvalue depending on the spectral gap of the dual Markov diffusion operator given by the intertwining. To see the relevance of our approach, we apply our spectral results in the case of perturbed product measures, freeing us from Helffer's classical method based on uniform spectral estimates for the one-dimensional conditional distributions.Read less <
ANR Project
Aux frontières de l'analyse Harmonique - ANR-12-BS01-0013
Stabilité du comportement asymptotique d'EDP, de processus stochastiques et de leurs discrétisations. - ANR-12-BS01-0019
Stabilité du comportement asymptotique d'EDP, de processus stochastiques et de leurs discrétisations. - ANR-12-BS01-0019
Origin
Hal imported