Field theory of Euclidean matrix ensembles

Recently, a class of Hermitian matrix ensembles was proposed by Mezard et al in which the matrix elements depend on the Euclidean separation of coordinates drawn from a random distribution. Matrix ensembles of this kind appear in a variety of physical contexts. In this paper, we formulate and investigate the spectral properties of these Euclidean random matrix ensembles within the framework of a supersymmetric statistical field theory. We discuss applications of these results to various model systems. (author)