  We present a new class of hermitian one-matrix models originated in the
W-infinity algebra: more precisely, the polynomials defining the W-infinity
generators in their fermionic bilinear form are shown to expand the orthogonal
basis of a class of random hermitian matrix models. The corresponding
potentials are given, and the thermodynamic limit interpreted in terms of a
simple plasma picture. The new matrix models can be successfully applied to the
full bosonization of interesting one-dimensional systems, including all the
perturbative orders in the inverse size of the system. As a simple application,
we present the all-order bosonization of the free fermionic field on the
one-dimensional lattice.
