# Intertwinings, second-order Brascamp-Lieb inequalities and spectral estimates

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 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.
Document type :
Preprints, Working Papers, ...
Domain :
Complete list of metadata

Cited literature [30 references]

https://hal.archives-ouvertes.fr/hal-01616432
Contributor : Aldéric Joulin <>
Submitted on : Friday, October 13, 2017 - 4:21:55 PM
Last modification on : Wednesday, June 9, 2021 - 10:00:10 AM
Long-term archiving on: : Sunday, January 14, 2018 - 1:54:42 PM

### Files

BJ_final.pdf
Files produced by the author(s)

### Identifiers

• HAL Id : hal-01616432, version 1
• ARXIV : 1710.08106

### Citation

Michel Bonnefont, Aldéric Joulin. Intertwinings, second-order Brascamp-Lieb inequalities and spectral estimates. 2017. ⟨hal-01616432⟩

Record views