Attracting Random Walks

We introduce the Attracting Random Walks model, which is an attractive interacting particle system. In the model, particles move between adjacent vertices of a graph G, with transition probabilities that depend positively on particle counts at neighboring vertices. From an applied standpoint, the model captures systems in which quantity is attractive. I will mention some possible applied areas, but the focus is on developing the properties of the associated Markov chain. The mixing time phase transition is of particular interest. When G is the complete graph, the model is a projection of the Potts model, whose phase transition is known. We demonstrate the existence of phase transition for general graphs.

 

(Joint work with David Gamarnik, Reza Gheissari, Patrick Jaillet, Eyal Lubetzky, Yuval Peres, and Yury Polyanskiy)