Concentration of measure and optimal transport

Series: 
Other Talks
Friday, May 20, 2011 - 15:05
1 hour (actually 50 minutes)
Location: 
Skiles 006
,  
University of Paris, Marne La Vallee
Organizer: 
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.