Persistence probability for a class of Gaussian processes related to random interface models

Abstract

We consider a class of Gaussian processes which are obtained as height processes of some (d + 1)-dimensional dynamic random interface model on Z^d. We give an estimate of persistence probability, namely, large T asymptotics of the probability that the process does not exceed a fixed level up to time T. The interaction of the model affects the persistence probability and its asymptotics changes depending on the dimension d.