Visit of professor Prasad TETALI

Prasad Tetali (Georgia Institute of Technology, Atlanta) has been  invited for a one month visit during the academic year 2011-2012. He worked with N. Gozlan, C. Roberto (Univ. Paris 10) and P.-M. Samson  on optimal transport  and its link with the Ricci curvature  on  discrete spaces. In Riemannian geometry, this subject attracted a lot of attention in recent years. However very few was known so far in discrete setting. As a result of this collaboration, the article « Displacement convexity of entropy and related inequalities on graphs » was published in 2014 in Probability Theory  and Related Fields. This paper  introduces a notion of an interpolating path on the set of probability  measures on finite graphs and  proves a displacement convexity  property of entropy along such  paths. Talagrand transport-entropy,  HWI and log-Sobolev type  inequalities are consequences  of this property in discrete settings. The  results of the paper  apply in particular  to the complete graph and  the hypercube.  After  this first joint work, Gozlan and Samson were invited by Tetali to attend  to three one week workshops entitled ”New directions in mass transport : discrete versus continuous ». As a result, several papers are submitted or in preparation.