Lifschitz tail and Wiener sausage, I

Abstract

The present paper is a continuation of [23]. We present here two examples of situations, where the method developed in [23] applies. The first example is that of a periodic diffusion (Z) in R”, n >, 1, with generator L = iSia,dj, where a,is a C2, Z”-periodic elliptic matrix. We consider the Wiener sausage W, = U0 c u < I Z, + C, where C is a nonpolar, . . compact subset of R”, for instance, a closed ball or disc in R”. If a denotes the constant matrix of homogenized coefficients of the periodic diffusion (see [ 1 I), we show that