Intertwinings, second-order Brascamp-Lieb inequalities and spectral estimates
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | BONNEFONT, Michel | |
| hal.structure.identifier | Institut de Mathématiques de Toulouse UMR5219 [IMT] | |
| dc.contributor.author | JOULIN, Aldéric | |
| dc.date.created | 2017 | |
| dc.description.abstractEn | 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. | |
| dc.description.sponsorship | Aux frontières de l'analyse Harmonique - ANR-12-BS01-0013 | |
| dc.description.sponsorship | Stabilité du comportement asymptotique d'EDP, de processus stochastiques et de leurs discrétisations. - ANR-12-BS01-0019 | |
| dc.language.iso | en | |
| dc.title.en | Intertwinings, second-order Brascamp-Lieb inequalities and spectral estimates | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math]/Probabilités [math.PR] | |
| dc.subject.hal | Mathématiques [math]/Analyse fonctionnelle [math.FA] | |
| dc.identifier.arxiv | 1710.08106 | |
| hal.identifier | hal-01616432 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01616432v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=BONNEFONT,%20Michel&JOULIN,%20Ald%C3%A9ric&rft.genre=preprint |
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