Zobrazeno 1 - 10
of 114
pro vyhledávání: '"Fathi Max"'
Autor:
Fathi Max, Le Bris Pierre, Menegaki Angeliki, Monmarche Pierre, Reygner Julien, Tomasevic Milica
Publikováno v:
ESAIM: Proceedings and Surveys, Vol 75, Pp 2-23 (2023)
This article presents a selection of recent results in the mathematical study of physical systems described by a large number of particles, with various types of interactions (mean-field, moderate, nearest-neighbor). Limit theorems are obtained conce
Externí odkaz:
https://doaj.org/article/3545c1f9a29e4664a86e8a2a1ab025a9
Autor:
Fathi, Max
We give an alternative proof and some extensions of results of Carlier, Figalli and Santambrogio on polynomial upper bounds on the Brenier map between probability measures under various conditions on the densities. The proofs are based on the monoton
Externí odkaz:
http://arxiv.org/abs/2407.11951
We give a new proof of the sharp symmetrized form of Talagrand's transport-entropy inequality. Compared to stochastic proofs of other Gaussian functional inequalities, the new idea here is a certain coupling induced by time-reversed martingale repres
Externí odkaz:
http://arxiv.org/abs/2407.09465
Autor:
Courtade, Thomas A., Fathi, Max
We resolve a question of Carrapatoso et al. on Gaussian optimality for the sharp constant in Poincar\'e-Korn inequalities, under a moment constraint. We also prove stability, showing that measures with near-optimal constant are quantitatively close t
Externí odkaz:
http://arxiv.org/abs/2405.01441
Autor:
Courtade, Thomas A., Fathi, Max
In a recent work, Klartag gave an improved version of Lichnerowicz' spectral gap bound for uniformly log-concave measures, which improves on the classical estimate by taking into account the covariance matrix. We analyze the equality cases in Klartag
Externí odkaz:
http://arxiv.org/abs/2404.12277
Caffarelli's contraction theorem states that probability measures with uniformly logconcave densities on R d can be realized as the image of a standard Gaussian measure by a globally Lipschitz transport map. We discuss some counterexamples and obstru
Externí odkaz:
http://arxiv.org/abs/2402.04649
Autor:
Courtade, Thomas A., Fathi, Max
HWI inequalities are interpolation inequalities relating entropy, Fisher information and optimal transport distances. We adapt an argument of Y. Wu for proving the Gaussian HWI inequality via a coupling argument to the discrete setting, establishing
Externí odkaz:
http://arxiv.org/abs/2312.01368
Publikováno v:
ESAIM: Proceedings and Surveys, Vol 48, Pp 341-363 (2015)
We consider in this work the numerical computation of transport coefficients for Brownian dynamics. We investigate the discretization error arising when simulating the dynamics with the Smart MC algorithm (also known as Metropolis-adjusted Langevin
Externí odkaz:
https://doaj.org/article/2dafa05f403340a0b1da8fc587eea469
We establish sufficient conditions for the existence of globally Lipschitz transport maps between probability measures and their log-Lipschitz perturbations, with dimension-free bounds. Our results include Gaussian measures on Euclidean spaces and un
Externí odkaz:
http://arxiv.org/abs/2305.03786
We study stability of the sharp spectral gap bounds for metric-measure spaces satisfying a curvature bound. Our main result, new even in the smooth setting, is a sharp quantitative estimate showing that if the spectral gap of an RCD$(N-1, N)$ space i
Externí odkaz:
http://arxiv.org/abs/2202.03769