Ed Perkins

We study a scaling limit of the long range SIR epidemic model in which infected individuals cannot be reinfected. The limit, which exists in up to 3 dimensions, has been studied by Lalley and Zheng and is reminiscent of a one-dimensional model...

We will study the edge of the support of 1-dimensional super-brownian motion. The local behaviour of the density, Hausdorff dimension of the boundary, and rates of convergence of certain solutions to singular semilinear heat equations studied in the...

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...