Reversible Growth Models on Z^d: Some Examples

Abstract

In a recent paper [3], a class of reversible growth models on a fairly general set of sites was introduced and studied. These models are generalizations of the finite reversible nearest particle systems on the integers, which have been considered in several papers in recent years (see [1] and [2], for example). The focus of attention in these growth models is the probability of survival of the system. Typically there are natural one parameter families of models, and one wishes to determine the critical value for that parameter, which is the point at which survival with positive probability begins to occur. Once this is done, it is of interest to determine the manner in which the survival probability approaches its limit (which is usually zero) as the parameter approaches the critical value from above.

Research supported in part by NSF Grant MCS 83–00836. This work was carried out at the Institute for Mathematics and its Applications at the University of Minnesota. Its hospitality is gratefully acknowledged.