  We study the spectrum of a random matrix, whose elements depend on the
Euclidean distance between points randomly distributed in space. This problem
is widely studied in the context of the Instantaneous Normal Modes of fluids
and is particularly relevant at the glass transition. We introduce a systematic
study of this problem through its representation by a field theory. In this way
we can easily construct a high density expansion, which can be resummed
producing an approximation to the spectrum similar to the Coherent Potential
Approximation for disordered systems.
