Title:Ergodic theory of the symmetric inclusion process
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