Evènement pour le groupe Combinatoire Énumérative et Algébrique

Date 2018-06-29  10:45-11:45
TitreInvariant measures of discrete interacting particle systems: algebraic aspects. 
RésuméParticle systems are a set of particles embedded in a graph, evolving randomly according to some politics. Among them we find the TASEP, the Contact process, the voter models and the zero range process. These are a particular type of continuous time Markov process; typically, the Markovian evolution is driven by some translation invariant local dynamics with bounded width dependence, encoded by a rate matrix T, meaning that the evolution of the particle at a given position depends only on the particles in a finite neighborhood of it and this evolution rule is invariant under translation. 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, …}. 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). We will show how these results give efficient ways to find Markovian invariant distributions for a given rate matrix or to prove that none exists. We will also present some applications on well known models and mild modifications of them.  
OrateurLuis Maximiliano Fredes Carrasco 

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