  We prove a large deviation result for a random symmetric n x n matrix with
independent identically distributed entries to have a few eigenvalues of size
n. If the spectrum S survives when the matrix is rescaled by a factor of n, it
can only be the eigenvalues of a Hilbert-Schmidt kernel k(x,y) on [0,1] x
[0,1]. The rate function for k is $I(k)=1/2\int h(k(x,y) dxdy$ where h is the
Cramer rate function for the common distribution of the entries that is assumed
to have a tail decaying faster than any Gaussian. The large deviation for S is
then obtained by contraction.
