Attracting Random Walks: Demos

Interacting random walks

Simulation on a grid graph

Two vertices

Profile of the stationary distribution for the two-vertex graph with n = 170 particles. The x-axis corresponds to the number of particles at vertex 1. For small attraction constants, we see particle spread, and for large attraction constants, we see aggregation. The attraction constant is parametrized as beta/n, and beta is labelled at the top.

Three vertices

Profile for the stationary distribution for the triangle graph. Each corner of the probability simplex corresponds to placing all n particles at a single vertex. Again, beta is labelled.

gaudio [at] mit [dot] edu




Google Scholar

mit logo

orc logo