Probability Seminar: Edwin Perkins

  • Date: 03/20/2019
  • Time: 15:00
Edwin Perkins, UBC

University of British Columbia


On the range of lattice models in high dimensions


We investigate the scaling limit of the range (the set of visited vertices) for a general class of critical lattice models, starting from a single initial particle at the origin.  Conditions are given on the random sets and an associated ``ancestral relation" under which, conditional on long-term survival, the rescaled ranges converge weakly to the range of super-Brownian motion as random sets. These hypotheses also give precise asymptotics for the limiting behaviour of the probability of exiting a large ball. Applications include voter models, contact processes, oriented percolation and lattice trees.  This is joint work with Mark Holmes and also features work of Akira Sakai and Gord Slade.

Other Information: 

Location: ESB 1012