On the stationary measures of two variants of the voter model.

Resumen: The voter model is an interacting particle system describing the collective behaviour of voters who constantly update their political opinions on a given graph. This Markov process is dual to a system of coalescing random walks on the graph. This duality relationship makes the model more tractable by analysing the dynamics of the collision of random walks.

This presentation is divided into two parts. First, we introduce two variants of the voter model: the voter model on dynamical percolation (in a random environment) and the voter model with stirring (where a stirring parameter introduces the dynamic exchange of opinions between neighboring sites). Obtaining their respective coalescing random walk variations, we obtain a characterization of the set of stationary measures.

Posted on Nov 19, 2024 in Seminario de Probabilidades de Chile, Seminars