Journal of Applied Mathematics and Stochastic Analysis
Volume 9 (1996), Issue 4, Pages 531-549

Balls left empty by a critical branching Wiener process

Pál Révész

Technische Universität Wien, Institut für Statistik und Wahrscheinlichkeitstheorie, Wien A-1040, Austria

Received 1 July 1996; Revised 1 October 1996

Copyright © 1996 Pál Révész. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


At time t=0 we have a Poisson random field on d. 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 d which does not contain any particle at time T. Our goal is to characterize the properties of the stochastic process {RT,T0}.

This article is dedicated to the memory of Professor Roland L. Dobrushin.