Invariant measures of discrete interacting particle systems: Algebraic aspects

Abstract:

We consider a continuous time particle system on a graph L being either Z,  Z_n, a segment {1,…, n}, or Z^d, with state space Ek={0,…,k-1} for some k belonging to {infinity, 2, 3, …}. We also assume that the Markovian evolution is driven by some translation invariant local dynamics with bounded width dependence, encoded by a rate matrix T. These are standard settings, satisfied by many studied particle systems. We provide some sufficient and/or necessary conditions on the matrix T, so that this Markov process admits some simple invariant distribution, as a product measure, as the distribution of a Markov process indexed by Z or {1,…, n} (if L=Z or {1,…,n}), or as a Gibbs measure (if L=Z_n). These results are mainly obtained with some manipulations of finite words, with alphabet Ek, representing subconfigurations of the systems. For the case L=Z, we give a procedure to find the set of invariant i.i.d and Markov measures.

Date: Jan 09, 2018 at 15:00 h
Venue: Beauchef 851, Torre Norte, 7mo Piso, Sala de Seminarios John Von Neumann CMM.
Speaker: Luis Fredes
Affiliation: Bordeaux
Coordinator: Daniel Remenik
Abstract:
PDF

Posted on Jan 3, 2018 in Núcleo Modelos Estocásticos de Sistemas Complejos y Desordenados, Seminars