  We show that there exists a simple generalization of Kazakov's multicritical
one-matrix model, which interpolates between the various multicritical points
of the model. The associated multicritical potential takes the form of a power
series with a heavy tail, leading to a cut of the potential and its derivative
at the real axis, and reduces to a polynomial at Kazakov's multicritical
points. From the combinatorial point of view the generalized model allows
polygons of arbitrary large degrees (or vertices of arbitrary large degree,
when considering the dual graphs), and it is the weight assigned to these large
order polygons which brings about the interpolation between the multicritical
points in the one-matrix model.
