GENERALIZED KONTSEVICH MODEL VERSUS TODA HIERARCHY AND DISCRETE MATRIX MODELS

We present the partition function of the Generalized Kontsevich Model (GKM) in the form of a Toda lattice tau-function and discuss various i mplications of non-vanishing ''negative-time'' and ''zero-time'' varia bles: they appear to modify the original GKM action by negative-power and logarithmic contributions, respectively. It is shown that such a d eformed tau-function satisfies the same string equation as the origina l one. In the case of quadratic potentials GKM turns out to describe f orced Toda chain hierarchy and thus corresponds to a discrete matrix m odel, with the role of matrix size played by the zero-time (at integer positive points). This relation allows one to discuss the double-scal ing continuum limit entirely in terms of GKM, i.e. essentially in term s of finite-fold integrals.