  In this paper we construct a class of random matrix ensembles labelled by a
real parameter $\alpha \in (0,1)$, whose eigenvalue density near zero behaves
like $|x|^\alpha$. The eigenvalue spacing near zero scales like
$1/N^{1/(1+\alpha)}$ and thus these ensembles are representatives of a {\em
continous} series of new universality classes. We study these ensembles both in
the bulk and on the scale of eigenvalue spacing. In the former case we obtain
formulas for the eigenvalue density, while in the latter case we obtain
approximate expressions for the scaling functions in the microscopic limit
using a very simple approximate method based on the location of zeroes of
orthogonal polynomials.
