9703811 Sethuraman The fluctuation behavior of a single, or "tagged" particle moving in certain asymmetric stochastic dynamical systems is studied. The stochastic systems fall into two model classes: Conservative particle systems, and Brownian trapping models. The first category includes the simple exclusion and zero-range systems, while the second category considers variants of the "Wiener Sausage" model. An important difference between these two classes lies in that the random environments presented to a particular particle are "changing in a comparable scale" in the first and "slowly varying" in the second. Although the tagged particle fluctuations are well understood with respect to reversible versions of these models, little is known when these processes possess a drift. This project focuses on developing various estimates and limit theorems which do not depend on symmetry, so as to identify the non-reversible tagged particle fluctuation picture. Two sample questions which are addressed in this work are: What are the effective statistics governing the behavior of a typical passenger interacting with other passengers moving in a complex Customs queue? Consider a thick porous stone roof of a cave; what is the chance that a rain drop will weave its way through the fissures in the stone to drip into the cave, and what strategy does it take to avoid being absorbed into the stone? These two questions fit into the framework of the so-called "tagged" particle problem which is the main subject of this project. Abstractly, a particle, such as a passenger or a rain drop, interacts with a random environment. The goal of this project is to understand the fluctuation probabilities of this particle interaction in various systems with asymmetries. The motivation for this work is that the most general situations in many physical phenomena of interest, such as fluid flow, queuing, and chemical ion trapping behavior, are well modeled by these asymmetric p rocesses. The significance of this project is that asymmetry is a main feature of the models considered; previously, research proceeded under the less palatable assumption of symmetry which often simplified the models beyond application.
