53 research outputs found
Characterization of Talagrand's Like Transportation-Cost Inequalities on the Real Line
In this paper, we give necessary and sufficient conditions for Talagrand's
like transportation cost inequalities on the real line. This brings a new wide
class of examples of probability measures enjoying a dimension-free
concentration of measure property. Another byproduct is the characterization of
modified Log-Sobolev inequalities for Log-concave probability measures on R
Poincar\'e inequality for non euclidean metrics and transportation cost inequalities on
In this paper, we consider Poincar\'e inequalities for non euclidean metrics
on . These inequalities enable us to derive precise dimension
free concentration inequalities for product measures. This technique is
appropriate for a large scope of concentration rate: between exponential and
gaussian and beyond. We give different equivalent functional forms of these
Poincar\'e type inequalities in terms of transportation-cost inequalities and
infimum convolution inequalities. Workable sufficient conditions are given and
a comparison is made with generalized Beckner-Latala-Oleszkiewicz inequalities
Transport-entropy inequalities on the line
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 verifying Talagrand's T2 inequality and not the
logarithmic Sobolev inequality
Transport Inequalities. A Survey
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 their links with other functional
inequalities and also large deviation theory.Comment: Proceedings of the conference Inhomogeneous Random Systems 2009; 82
pages
On A Mixture Of Brenier and Strassen Theorems
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 transport given by the gradient of a
continuously differentiable convex function followed by a martingale coupling.
We also establish some connections with Caffarelli's contraction theorem [14]
Inégalités fonctionnelles, transport optimal et grandes déviations
Ce document présente une synthèse des travaux menés sur les inégalités fonctionnelles et leurs liens avec le phénomène de concentration de la mesure
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