# Convex relative entropy decay in Markov chains

 Speaker : Venkat Anantharam University of California, Berkeley Date: 11/06/2014 Time: 3:30 pm - 4:30 pm Location: LINCS Meeting Room 40

### Abstract

Consider an irreducible continuous time Markov chain with a finite or a countably infinite number of states and admitting a unique stationary probability distribution. The relative entropy of the distribution of the chain at any time with respect to the stationary distribution is a monotonically decreasing function of time. It is interesting to ask if this function is convex. We discuss this question for finite Markov chains and for Jackson networks, which are a class of countable state Markov chains of interest in modeling networks of queues. (Joint work with Varun Jog.)