86 citations · 350 across the 38 of their papers we have counts for
29 papers · 1 filter
Generalized Wasserstein barycenters between probability measures living on different subspaces
Julie Delon, Nathaël Gozlan, Alexandre Saint-Dizier
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 existe…
Transport inequalities for random point measures
Nathael Gozlan, Ronan Herry, Giovanni Peccati
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 t…
Log-Hessian and Deviation Bounds for Markov Semi-Groups, and Regularization Effect in
Nathael Gozlan, Xue-Mei Li, Mokshay Madiman +2
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 hyperc…
Transport Proofs Of Some Discrete Variants Of The Pr{é}Kopa-leindler Inequality
Nathael Gozlan, Cyril Roberto, Paul-Marie Samson +1
We give a transport proof of a discrete version of the displacement convexity of entropy on integers (Z), and get, as a consequence, two discrete forms of the Pr{é}kopa-Leindler In…
A proof of the Caffarelli contraction theorem via entropic regularization
Max Fathi, Nathael Gozlan, Maxime Prodhomme
We give a new proof of the Caffarelli contraction theorem, which states that the Brenier optimal transport map sending the standard Gaussian measure onto a uniformly log-concave pr…
On A Mixture Of Brenier and Strassen Theorems
Nathael Gozlan, Nicolas Juillet
We give a characterization of optimal transport plans for a variant of the usual quadratic transport cost introduced in [33]. Optimal plans are composition of a deterministic trans…