Algèbres de von Neumann et matrices aléatoires
Tue, Jun. 07th 2011, 11:00
Salle Claude Itzykson, Bât. 774, Orme des Merisiers
Voiculescu showed how the large N limit of the expected value of the trace of a word on n independent hermitian matrices gives a well known von Neumann algebra. In joint work with Guionnet and Shlyakhtenko it was shown that this idea makes sense in the context of very general planar algebras where one works directly in the large N limit. This allowed us to define matrix models with a non-integral number of random matrices. I will present this work and some of the subsequent work, together with future hopes for the theory.