Mathematical Sciences: Studies in Interacting Particle Systems and Brownian Motion

小行星9400644 教授Liggett，芒福德和Schonmann将在几个项目相关的两个领域的概率论：相互作用的粒子系统和布朗运动。其中第一个是研究概率模型的演变大型物理系统经历相变，而第二个是一个更经典的模型，发挥了核心作用的概率为大部分的这世纪。在第一个领域要考虑的问题是：获得良好的界限上的临界值，分离的单相多相参数区域，并确定收敛到平衡的几个模型，包括随机伊辛模型和最近的粒子系统的速度。在第二个领域，详细的布朗单的水平集的性质将被调查。 概率论中一个相对较新且非常活跃的领域被称为相互作用粒子系统。它致力于分析物理系统演化的概率模型，这些物理系统可以处于两个或多个阶段-例如金属（磁化或未磁化）或水（冰，水，蒸汽）。 这一领域的一些研究结果也可应用于其他领域，如队列和疾病传播的研究。教授Liggett，芒福德和Schonmann将继续他们的工作在这个领域的一些基本问题。其中之一是确定物理参数（温度，压力等）的区域。其中各种相发生，以及系统在相描述改变的点附近的行为。另一个是研究系统接近平衡的速度。

9400644 Liggett Professors Liggett, Mountford and Schonmann will work on several projects related to two areas of Probability Theory: Interacting Particle Systems and Brownian Motion. The first of these is the study of probabilistic models for the evolution of large physical systems which undergo phase transitions, while the second is a more classical model which has played a central role in Probability for much of this century. Among the problems to be considered in the first area are: obtaining good bounds on the critical values which separate the single phase from the multiphase parameter region, and determining rates of convergence to equilibrium in several models, including the stochastic Ising model and nearest particle systems. In the second area, detailed properties of the level sets of the Brownian sheet will be investigated. A relatively new and very active area of Probability Theory is known as Interacting Particle Systems. It is devoted to the analysis of probabilistic models for the evolution of physical systems which can be in two or more phases - pieces of metal (magnetized or not) or water (ice, water, steam) for example. Some results of investigations in this area also have applications in other areas, such as the study of queues and transmission of disease. Professors Liggett, Mountford and Schonmann will continue their work on some of the basic problems in this field. One of them is the determination of the regions of physical parameters (temperature, pressure, etc.) in which various phases occur, and the behavior of the systems near points at which the phase description changes. Another is a study of the speed with which systems approach equilibrium.