A new class of matrix models arising from the W1+∞ algebra

We present a new class of Hermitian one-matrix models originated in the W1+∞ algebra: more precisely, the polynomials defining the W1+∞ 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.