|Location:||MSRI: Simons Auditorium|
Relying on its representation as a solution of certain
Schwinger-Dyson equation, we study the low temperature
expansion of the limiting spectral measure
(and limiting free energy), for random matrix models, in case of potentials which are strictly convex
in some neighborhood of each of their finitely many
local minima. When applied to suitable polynomial test
functions, these expansions are given in terms of
the aboslutely convergent generating function
of an interesting class of colored maps.
This talk is based on a joint work with
Alice Guionnet and Edouard Maurel-Segala.