Fluctuations in Asymmetric Processes with Static and Dynamic Random Environments

小行星9703811 一个单一的，或“标记”的粒子在一定的运动波动行为， 研究了非对称随机动力系统。 随机系统分为两类 模型类别：保守粒子系统和布朗捕获模型。 第一 第一类包括简单排除和零范围系统，而第二类包括简单排除和零范围系统。 考虑“维纳香肠”模型的变体。 这两者之间的一个重要区别是 两类在于，呈现给特定粒子的随机环境是 第一种是“规模相当的变化”，第二种是“缓慢变化”。虽然 标记粒子的波动相对于 这些模型，很少有人知道，当这些过程具有漂移。 该项目的重点是 发展各种不依赖于对称性的估计和极限定理， 来识别不可逆的标记粒子波动图像。 在这项工作中解决的两个问题是：什么是有效的 管理典型乘客与其他乘客互动行为的统计数据 在复杂的海关队列中移动？考虑一个厚厚的多孔石头屋顶的洞穴;什么 就是一滴雨水会穿过石头的裂缝滴下来 进入洞穴，需要采取什么策略来避免被吸收到石头里？ 这两个问题符合所谓的“标记”粒子问题的框架 这是本项目的主要课题。 抽象地说，一个粒子，如乘客或 雨滴与随机环境相互作用。 这个项目的目标是了解 这种粒子相互作用在各种系统中的波动概率， 不对称 这项工作的动机是，在许多情况下， 感兴趣的物理现象，如流体流动、排队和化学离子捕获 行为，很好地模拟了这些不对称的过程。 其意义 项目是，不对称是考虑模型的主要特征;以前，研究 在不太令人愉快的对称假设下进行，这种假设往往简化了 超越应用的模式

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.