24 citations · 70 across the 15 of their papers we have counts for
16 papers
On the quadratic barycentric transport problem
Nathael Gozlan, Thibaut Le Gouic, Paul-Marie Samson
We investigate the structure of optimal transport plans, dual optimizers, and geodesic paths for the quadratic barycentric transport problem.
Criteria for entropic curvature on graph spaces
Martin Rapaport, Paul-Marie Samson
In this paper we establish new simple local geometric criteria for discrete entropic curvature introduced in [47] that are powerful enough to capture many geometric properties of c…
Entropic curvature on graphs along Schr{ö}dinger bridges at zero temperature
Paul-Marie Samson
Lott-Sturm-Villani theory of curvature on geodesic spaces has been extended to discrete graph spaces by C. L{é}onard by replacing W2-Wasserstein geodesics by Schr{ö}odinger bridges…
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…
Deviation inequalities for convex functions motivated by the Talagrand conjecture
Nathael Gozlan, Mokshay Madiman, Cyril Roberto +1
Motivated by Talagrand's conjecture on regularization properties of the natural semigroup on the Boolean hypercube, and in particular its continuous analogue involving regularizati…
Transport-entropy inequalities on locally acting groups of permutations
Paul-Marie Samson
Following Talagrand's concentration results for permutations picked uniformly at random from a symmetric group [Tal95], Luczak and McDiarmid have generalized it to more general gro…
Characterization of a class of weak transport-entropy inequalities on the line
Nathael Gozlan, Cyril Roberto, Paul-Marie Samson +2
We study an optimal weak transport cost related to the notion of convex order between probability measures. On the real line, we show that this weak transport cost is reached for a…
Kantorovich duality for general transport costs and applications
Nathael Gozlan, Cyril Roberto, Paul-Marie Samson +1
We introduce a general notion of transport cost that encompasses many costs used in the literature (including the classical one and weak transport costs introduced by Talagrand and…
Bounds on the deficit in the logarithmic Sobolev inequality
Sergey Bobkov, Nathael Gozlan, Cyril Roberto +1
The de cit in the logarithmic Sobolev inequality for the Gaussian measure is considered and estimated by means of transport and information-theoretic distances.
From dimension free concentration to Poincaré inequality
Nathael Gozlan, Cyril Roberto, Paul-Marie Samson
We prove that a probability measure on an abstract metric space satisfies a non trivial dimension free concentration inequality for the metric if and only if it satisfies…
Displacement convexity of entropy and related inequalities on graphs
Nathaël Gozlan, Cyril Roberto, Paul-Marie Samson +1
We introduce the notion of an interpolating path on the set of probability measures on finite graphs. Using this notion, we first prove a displacement convexity property of entropy…
Hamilton Jacobi equations on metric spaces and transport-entropy inequalities
Nathael Gozlan, Cyril Roberto, Paul-Marie Samson
We prove an Hopf-Lax-Oleinik formula for the solutions of some Hamilton- Jacobi equations on a general metric space. As a first consequence, we show in full gener- ality that the l…
Characterization of Talagrand's transport-entropy inequalities in metric spaces
Nathaël Gozlan, Cyril Roberto, Paul-Marie Samson
We give a characterization of transport-entropy inequalities in metric spaces. As an application we deduce that such inequalities are stable under bounded perturbation (Holley-Stro…
A new characterization of Talagrand's transport-entropy inequalities and applications
Nathael Gozlan, Cyril Roberto, Paul-Marie Samson
We show that Talagrand's transport inequality is equivalent to a restricted logarithmic Sobolev inequality. This result clarifies the links between these two important functional i…
The Logarithmic Sobolev Constant of The Lamplighter
Evgeny Abakumov, Anne Beaulieu, François Blanchard +17
We give estimates on the logarithmic Sobolev constant of some finite lamplighter graphs in terms of the spectral gap of the underlying base. Also, we give examples of application.