Zobrazeno 1 - 10
of 114
pro vyhledávání: '"Gozlan, Nathael"'
We reveal the relation between the Legendre transform of convex functions and heat flow evolution, and how it applies to the functional Blaschke-Santalo inequality. We also describe local maximizers in this inequality.
Externí odkaz:
http://arxiv.org/abs/2403.15357
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
We explore alternative functional or transport-entropy formulations of the Blaschke-Santal{\'o} inequality and of its conjectured counterpart due to Mahler. In particular, we obtain new direct and reverse Blaschke-Santal{\'o} inequalities for s-conca
Externí odkaz:
http://arxiv.org/abs/2307.04393
We introduce a new variant of the weak optimal transport problem where mass is distributed from one space to the other through unnormalized kernels. We give sufficient conditions for primal attainment and prove a dual formula for this transport probl
Externí odkaz:
http://arxiv.org/abs/2203.16227
In this paper, we present a simple proof of a recent result of the second author which establishes that functional inverse-Santal{\'o} inequalities follow from Entropy-Transport inequalities. Then, using transport arguments together with elementary c
Externí odkaz:
http://arxiv.org/abs/2109.00871
In this paper, we introduce a generalization of the Wasserstein barycenter, to a case where the initial probability measures live on different subspaces of R^d. We study the existence and uniqueness of this barycenter, we show how it is related to a
Externí odkaz:
http://arxiv.org/abs/2105.09755
Autor:
Gozlan, Nathaël
We establish dual equivalent forms involving relative entropy, Fisher information and optimal transport costs of inverse Santal{\'o} inequalities. We show in particular that the Mahler conjecture is equivalent to some dimensional lower bound on the d
Externí odkaz:
http://arxiv.org/abs/2007.05255
We derive transport-entropy inequalities for mixed binomial point processes, and for Poisson point processes. We show that when the finite intensity measure satisfies a Talagrand transport inequality, the law of the point process also satisfies a Tal
Externí odkaz:
http://arxiv.org/abs/2002.04923
Publikováno v:
Potential Analysis 58, 123-158 (2023)
It is well known that some important Markov semi-groups have a "regularization effect" -- as for example the hypercontractivity property of the noise operator on the Boolean hypercube or the Ornstein-Uhlenbeck semi-group on the real line, which appli
Externí odkaz:
http://arxiv.org/abs/1907.10896