Concentration of measure and optimal transport

Other Talks
Friday, May 20, 2011 - 15:05
1 hour (actually 50 minutes)
Skiles 006
University of Paris, Marne La Vallee
The aim of this talk is to present recent results obtained in collaboration with C. L\'eonard, C. Roberto and P.M Samson. In the first part, I will give a necessary and sufficient condition for Talagrand's inequality on the  real line. In the second part, I will explain the links between Talagrand's inequality and the dimension-free Gaussian concentration phenomenon. This will lead  us to a new proof of Otto-Villani Theorem. Finally, in the third part, we will show that Talagrand's  inequality is equivalent to a variant of the log-Sobolev inequality, called the inf-convolution log-Sobolev inequality. This theorem will enable us to prove a general perturbation result for Talagrand's  inequality.