Mathematics Colloquium, Fall 2004

Double scaling limit in random matrix models and a nonlinear hierarchy of differential equations

Partition functions of random matrix models provide generating functions for a number of combinatorial and physical problems: enumeration of graphs on Riemannian surfaces and quantum gravity, spin models of statistical mechanics on random surfaces, enumeration of knots and links, meanders, and others. Critical points and double scaling limits of random matrix models determine in this context the large N asymptotics of the quantities under consideration. In the talk we will discuss critical phenomena for random matrix models and relate the double scaling limit at critical points to the Painlev\'e II nonlinear hierarchy of differential equations.

Thursday, December 2, 2004, 245 Altgeld Hall, 4 p.m.