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.
