The short-time limit of the Dirichlet partition function and the image method

Abstract

In this paper we rigorously derive the t → 0+ asymptotics of the free partition function ZΩ(t) for a diffusion process on tessellations of the d-dimensional Euclidean space , d = 1, 2, 3 with an absorbing boundary. Utilising the path integral approach and the method of images for domains which are compatible with finite reflection subgroups of the orthogonal group , we solve this problem following a group theoretic method which was lacking from the literature.