Sydney Dynamics Group Seminar: Upanshu Sharma, University of New South Wales -- Sydney Dynamics group Seminar

Seminar : Sydney Dynamics group Seminar 
Day/time : Thursday, April 30 at 4:00 PM,
Location : SMRI seminar room (A12 Macleay Room 301) 
Speaker : Upanshu Sharma, UNSW 

Title: Non-equilibrium functional inequalities for finite Markov chains 

Abstract: Functional inequalities such as the Poincaré and log-Sobolev inequalities
quantify convergence to equilibrium in continuous-time Markov chains (and more generally
Markov processes) by linking properties of the generator to variance and entropy decay.
However, in certain applications, such as coarse-graining problems arising in molecular
dynamics, it becomes necessary to study entropy decay with respect to a reference
measure that is not the steady state.  In such settings, the dynamics are typically
non-reversible (i.e.  not of gradient-flow type), and the classical functional
inequality framework tied to equilibrium does not directly apply.  

In this talk, I will introduce a generalisation of the log-Sobolev inequality with
respect to arbitrary probability measures on a finite state space.  This generalisation
retains key features of the classical inequality while exhibiting properties relevant
for coarse-graining applications, including continuity with respect to the reference
measure and explicitly computable lower bounds.  If time permits, as an application I
will use this generalisation to derive quantitative error bounds for coarse-graining of
finite Markov chains.  

This talks is based on joint work with Bastian Hilder and Patrick van Meurs.