Dimitri Shlyakhtenko (4.1) Random matrices and free probability, part 4.1
Channel: IAS | Park City Mathematics Institute | PCMI
Date: 2017-07-01

Dimitri Shlyakhtenko, University of California, Los Angeles. Lecture notes available at https://pcmi.ias.edu/sites/pcmi.ias.edu/files/Dimitri%20Shlyakhtenko%20Lecture%20Notes.pdf

Voiculescu invented his free probability theory to approach problems in von Neumann algebras. A key feature of his theory is the treatment of free independence — based on the notion of free products, such as free products of groups — as a surprisingly close parallel to classical independence. Rather unexpectedly it turned out that there are deep connections between his theory and the theory of random matrices: very roughly, free probability describes certain aspects of asymptotic behavior of random matrix models. In this course, we will start with an introduction to free probability theory, discuss connections with random matrix theory, and finally describe some applications of results from random matrices in operator algebras and vice versa.

Presented at the 27th Annual PCMI Summer Session, Random Matrices, held June 25 – July 15, 2017. The residential, three-week Summer Session is the flagship activity of the IAS/Park City Mathematics Institute (PCMI).

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