Ricci curvature for finite Markov chains

Series: 
PDE Seminar
Tuesday, November 19, 2013 - 15:05
1 hour (actually 50 minutes)
Location: 
Skiles 006
,  
University of Bonn
In this talk I will present a new notion of Ricci curvature that applies to finite Markov chains and weighted graphs. It is defined using tools from optimal transport in terms of convexity properties of the Boltzmann entropy functional on the space of probability measures over the graph. I will also discuss consequences of lower curvature bounds in terms of functional inequalities. E.g. we will see that a positive lower bound implies a modified logarithmic Sobolev inequality. This is joint work with Jan Maas.