Probability Seminar: Eric Foxall

  • Date: 01/22/2020
  • Time: 15:15
Eric Foxall, UBC - Okanagan

University of British Columbia


Clustering in the three and four colour cyclic particle systems in one dimension


We study the κ-color cyclic particle system on the one-dimensional integer lattice, first introduced by Bramson and Griffeath. In their original article they show that almost surely, every site changes its color infinitely often if κ ∈ {3, 4} and only finitely many times if κ ≥ 5. In addition, they conjecture that for κ ∈ {3, 4} the system clusters, that is, for any pair of sites x, y, with probability tending to 1 as t → ∞, x and y have the same color at time t. Here we prove that conjecture.

Joint work with Hanbaek Lyu.

Other Information: 

Location:  ESB 4133