Law of Large Numbers for Wiener Measure with Density Having Two Large Deviation Minimizers

Abstract

This paper discusses the situation that the large deviation rate functional has two distinct minimizers, for a model described by Wiener measures with certain densities involving a scaling. The motivation comes from the study of the so-called $\nabla\varphi$ interface model with weak self potentials. The pinned Wiener measures case was discussed by [3].