Balls left empty by a critical branching Wiener process

Abstract

At time t=0 we have a Poisson random field on ℝd. Each particle executes a critical branching Wiener process starting from its position at time t=0. Let RT be the radius of the largest ball around the origin of ℝd which does not contain any particle at time T. Our goal is to characterize the properties of the stochastic process {RT,T≥0}.This article is dedicated to the memory of Professor Roland L. Dobrushin.