Free probability, free entropy and applications to von Neumann algebras

Abstract

This talk is organized as follows: First we explain some basic concepts in non-commutative probability theory in the frame of operator algebras. In Section 2, we discuss related topics in von Neumann algebras. Sections 3 and 4 contain some of the key ideas and results in free probability theory. Last section states some of the important applications of free probability theory.

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• All generating sets of all property T von Neumann algebras have free entropy dimension $\le 1$