Equivalence between dimensional contractions in Wasserstein distance and the curvature-dimension condition

Autor: Ivan Gentil, Arnaud Guillin, François Bolley, Kazumasa Kuwada

Publikováno v: Annali della Scuola Normale Superiore di Pisa
Annali della Scuola Normale Superiore di Pisa, 2018, 18 (4), pp.1-36

International audience; The curvature-dimension condition is a generalization of the Bochner inequality to weighted Riemannian manifolds and general metric measure spaces. It is now known to be equivalent to evolution variational inequalities for the

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3499037b78f87f88bbaeee510fd699fa
https://doi.org/10.2422/2036-2145.201611_009

Dynamics of a planar Coulomb gas

Autor: François Bolley, Joaquin Fontbona, Djalil Chafaï

Publikováno v: Annals of Applied Probability
Annals of Applied Probability, Institute of Mathematical Statistics (IMS), 2018, 28 (5), pp.3152-3183. ⟨10.1214/18-AAP1386⟩
Ann. Appl. Probab. 28, no. 5 (2018), 3152-3183

We study the long-time behavior of the dynamics of interacting planar Brow-nian particles, confined by an external field and subject to a singular pair repulsion. The invariant law is an exchangeable Boltzmann -- Gibbs measure. For a special inverse

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5b9e31ea57acf9cac5e06f931c217cdd
https://hal.archives-ouvertes.fr/hal-01546288v4/document

New sharp Gagliardo-Nirenberg-Sobolev inequalities and an improved Borell-Brascamp-Lieb inequality

Autor: François Bolley, Dario Cordero-Erausquin, Yasuhiro Fujita, Arnaud Guillin, Ivan Gentil

Publikováno v: International Mathematics Research Notices
International Mathematics Research Notices, Oxford University Press (OUP), In press, pp.3042-3083
International Mathematics Research Notices, In press, 2020 (10), pp.3042-3083. ⟨10.1093/imrn/rny111⟩

We propose a new Borell–Brascamp–Lieb inequality that leads to novel sharp Euclidean inequalities such as Gagliardo–Nirenberg–Sobolev inequalities in $ {\mathbb{R}}^n$ and in the half-space $ {\mathbb{R}}^n_+$. This gives a new bridge between

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c64a375689c5566ff88763379ae20559
http://arxiv.org/abs/1702.03090

Dimension dependent hypercontractivity for Gaussian kernels

Autor: François Bolley, Dominique Bakry, Ivan Gentil

Publikováno v: Probability Theory and Related Fields
Probability Theory and Related Fields, Springer Verlag, 2012, 154 (3-4), pp.845-874. ⟨10.1007/s00440-011-0387-y⟩
Probability Theory and Related Fields, 2012, 154 (3-4), pp.845-874. ⟨10.1007/s00440-011-0387-y⟩

We derive sharp, local and dimension dependent hypercontractive bounds on the Markov kernel of a large class of diffusion semigroups. Unlike the dimension free ones, they capture refined properties of Markov kernels, such as trace estimates. They imp

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::00afd700af96b5e15772a5732ffcdc73
https://doi.org/10.1007/s00440-011-0387-y

Concentration of measure on product spaces with applications to Markov processes

Autor: Gordon Blower, François Bolley

Publikováno v: Studia Mathematica. 175:47-72

For a stochastic process with state space some Polish space, this paper gives sufficient conditions on the initial and conditional distributions for the joint law to satisfy Gaussian concentration and transportation inequalities. In the case of Eucli

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::4e2c13fa70be3544c50641e68ec44c04
https://doi.org/10.4064/sm175-1-3