Generation of matrix models by W-circumflex -operators

We show that partition functions of various matrix models can be obtained by acting on elementary functions with exponents of W-circumflex operators. A number of illustrations is given, including the Gaussian Hermitian matrix model, Hermitian model in external field and the Hurwitz-Kontsevitch model, for which we suggest an elegant matrix-model representation. In all these examples, the relevant W-circumflex operators belong to the W-circumflex (3) algebra.