Spectra of euclidean random matrices

We study the spectrum of a random matrix, whose elements depend on the eucl idean distance between points randomly distributed in space. This problem i s widely studied in the context of the Instantaneous Normal Modes of fluids and is particularly relevant at the glass transition. We introduce a syste matic study of this problem through its representation by a field theory. I n this way we can easily construct a high density expansion, which can be r esummed producing an approximation to the spectrum similar to the Coherent Potential Approximation for disordered systems. (C) 1999 Published by Elsev ier Science B.V. All rights reserved.