Graduate Seminar Analysis

 

Tuesday, March 8, 2018, 10:30am

Quantifying coarse-graining error

Upanshu Sharma, CERMICS, École des Ponts ParisTech

Abstract: Coarse-graining or dimension reduction is the procedure of approximating a large and complex system by a simpler and lower-dimensional one. A key feature that allows for such an approximation is a choice to consider only part of information by means of a coarse-graining map F that is strongly many-to-one. Assuming that the configuration of the full system is governed by a stochastic differential equation (SDE), for, say, a random variable X (representing for instance the position of particles in the system), Gyöngy postulated an ‘closed' evolution equation for the reduced (coarse grained) variable F(X), which is again a stochastic differential equation with coefficients derived from the full one. While lower dimensional this evolution is difficult to work with numerically. Legoll and Lelièvre proposed an approximation to this evolution and showed in the case of one-dimensional coarse-graining maps F and starting with reversible SDEs how to estimate the error of this approximation.

In this talk, I will present recent generalisations to a more general situations: (1) proving relative entropy estimates using a connection to large deviations and (2) pathwise estimates for non-reversible dynamics.

Location: Raum 203, Pontdriesch 14-16, 52062 Aachen