Korteweg-de Vries Institute for Mathematics

General Mathematics Colloquium

01June2016 11:15 - 12:15

Event

Speaker: Frank Redig (TU Delft)

Title:Ergodic theory  of the symmetric inclusion process

Abstract

We introduce the symmetric inclusion process, which is an interacting system where particles randomly hop over the lattice and interact by a specific mutual attraction between the particles. The model is of relevance in statistical physics (as the dual of a model of heat conduction), in population genetics as well as in econo-physics (models of wealth distribution). We show its connection to the SU(1,1) Casimir operator, and how from that follows a fundamental property, called self-duality.Using this property, we  show that characterizing invariant measures (with finite moments) boils down to showing that the only bounded harmonic functions of n inclusion walkers are constants.This in turn is achieved by constructing a successful coupling between two sets of n inclusion walkers, initially at different positions.

Based on joint work with Kevin Kuoch.
 

Location: KdVI meeting room, SP 105-107, F3.20

Published by  Korteweg de Vries Institute