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.
