Interacting Particle Systems and the Brownian Sheet

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0071471Mountford Professor Mountford will continue investigating interacting particle systems. Working in conjunction with Professor M. Bramson, he hopes to show the existence of "blocking measures" for the exclusion processes where the underlying random walk is finite range and possesses non-zero mean. If successful, they intend to examine the question of characterizing the extremal invariant measures for these processes. The key tool, the laws of large numbers of Rezakhanlou, will, it is to be hoped, also play a role in establishing convergence results for tandems of complicated Jackson networks. Professor Mountford will also continue his research with Professor R. Dalang into path properties of the Brownian sheet. In particular it is hoped to address how many distinct bubbles at a fixed (or a random level) can meet at a point. Professor Mountford will continue to work in the field of interacting particle systems. These are random systems consisting of an infinite array of connected values which evolve according to simple rules governed by the current state of neighboring values. What makes these processes interesting, both mathematically and scientifically, is that often there exist multiple, qualitatively different, equilibria for the same process. A major task is finding or characterizing all possible equilibria. Currently Professor Mountford is working on this question for the exclusion process. This is a process where particles try to move independently in a random fashion. The (interesting) interacting part of the process comes from the rule that no two particles can occupy the same position and so moves by particles that would result in multiple occupancy are suppressed.