Seminars and Events - Research Colloquia

Special Colloquia, Department of Statistics

Friday, January 12, 2001
3:30 PM in LAEB 1238

Mr. Jason Schweinsberg
University of California, Berkeley

will speak on

Coalescents with Simultaneous Multiple Collisions

Abstract

We will define a family of coalescent processes that undergo "simultaneous multiple collisions," which means that many clusters of particles can merge into a single cluster at one time, and many such mergers can occur simultaneously. This family of processes generalizes the "coalescents with multiple collisions" introduced by Pitman, in which many clusters of particles can merge into a single cluster at one time, but almost surely no two such mergers occur simultaneously. We will discuss how exchangeability considerations make it possible to characterize all coalescents with simultaneous multiple collisions. We will also indicate how these processes can arise as limits of ancestral processes. Finally, we will present a condition under which one of these coalescents "comes down from infinity", meaning that only finitely many clusters remain at all positive times even if the process begins with infinitely many particles at time zero.