Integrable systems, random matrices and random permutations
Pierre van Moerbeke
Abstract:
In this talk, I show that random matrix theory and random
permutation problems have suggested a number of new integrable systems,
e.g., the Pfaff Lattice and the Toeplitz lattice. They turn out to be very
useful at obtaining pde's for the probabilities in random matrix theory and
for the generating functions for the probabilities of the length of the
largest increasing sequences in random permutations.