Random matrix theory

Dedicated to the memory of Gert Kjærg˚ Pedersen ard Abstract In the process of developing the theory of free probability and free entropy, Voiculescu introduced in 1991 a random matrix model for a free semicircular system. Since then, random matrices have played a key role in von Neumann algebra theory (cf. [V8], [V9]). The main result of this paper is the follow(n) (n) ing extension of Voiculescu’s random matrix result: Let (X1 , . . . , Xr ) be a system of r stochastically independent n × n Gaussian self-adjoint random matrices as in Voiculescu’s random matrix paper...

66p noel_noel 17-01-2013 57 6   Download

We establish three identities involving Dyck paths and alternating Motzkin paths, whose proofs are based on variants of the same bijection. We interpret these identities in terms of closed random walks on the halfline. We explain how these identities arise from combinatorial interpretations of certain properties of the -Hermite and -Laguerre ensembles of random matrix theory. We conclude by presenting two other identities obtained in the same way, for which finding combinatorial proofs is an open problem....

16p thulanh5 12-09-2011 75 4   Download