  A random matrix approach to glassy physics is introduced. It leads to a class
of models which exhibit both, glassy low-temperature phases, and double-- and
single-well configurations in their potential energy. The distribution of
parameters characterizing the local potential energy configurations can be
computed, and differ from those assumed in the standard tunneling model and its
variants. Still, low-temperature anomalies characteristic of amorphous systems
are reproduced, and we are able to distinguish properties which can be expected
to be universal from those which cannot.
