Noncommutative Probability Aspects of Operator Algebra Theory

University Of California-Berkeley, Berkeley CA

Investigators

Abstract

Abstract Voiculescu Dan Voiculescu will study operator algebras in connection with free probability. He will emphasize applications of free entropy to operator algebras as well as the problems in operator algebras and random matrix theory posed by the development and unification of approaches to free entropy. There are also connections to masterfields in certain models in physics. Dan Voiculescu also intends to study noncommutative generalizations of the difference - quotient and of the Hilbert transform, in connection with duality for a certain class of coalgebras arising in free probability. Free probability theory is a highly noncommutative parallel to basic probability theory , modelling the asymptotic behavior of large random matrices as their size increases. One main focus will be on free entropy, the quantity which plays in this context the role of Shannon's information-theoretic entropy. Applications are in mathematics to von Neumann algebras and to random matrices, as well as to some models in physics .