45 citations · 48 across the 5 of their papers we have counts for
5 papers · 1 filter
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.
Transport proofs of weighted Poincaré inequalities for log-concave distributions
Dario Cordero-Erausquin, Nathael Gozlan
We prove, using optimal transport tools, weighted Poincar'e inequalities for log-concave random vectors satisfying some centering conditions. We recover by this way similar results…
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…
Transport-entropy inequalities on the line
Nathael Gozlan
We give a necessary and sufficient condition for transport-entropy inequalities in dimension one. As an application, we construct a new example of a probability distribution verify…
Transport Inequalities. A Survey
Nathael Gozlan, Christian Léonard
This is a survey of recent developments in the area of transport inequalities. We investigate their consequences in terms of concentration and deviation inequalities and sketch the…