Markovian fun with F

26/10/2018, 14:00 - 15:00 in MAP/0G/017

Köstler, Claus (Cork)


Abstract:

Markovianity is a stochastic phenomenon which does not care about the past – the presence ‘dictates’ the future. Unexpectedly this phenomenon is closely linked to representations of the Thompson group F. I will playfully introduce you to this new connection between randomness and symmetry. Toy examples are given by moving marbles on a two-dimensional grid. I will explain why this entails the general result that every stationary Markov chain induces a representation of the Thompson group F. Furthermore I will briefly address that, conversely, a large class of representations of F yields stationary Markov chains. Finally I will introduce ‘partial spreadability’ as a new distributional symmetry, aiming at a de Finetti type characterization of Markovianity. The presented results are based on ongoing research with Rajarama Bhat, Gwion Evans, Rolf Gohm, Arundhathi Krishnan, Vijaya Kumar, and Stephen Wills. My talk should be accessible to a general mathematical audience.