A Modified Domb-Joyce Model in Four Dimensions

#### S. Albeverio, X.Y. Zhou

1996, v.2, №3, 369-400

ABSTRACT

In this paper we discuss the asymptotic behaviour of some modified Domb-Joyce models in four dimensions, in which some weighted terms are removed from the original Domb-Joyce model. We prove that these modified models are tight, and in some special cases they are weakly convergent to the Wiener measure in $R^4$.

Keywords: Polymer measure,Wiener measure,Domb-Joyce model,intersections of random walks