Скачать или смотреть Persi Diaconis-FROM RANDOM MATRIX THEORY TO TOEPLITZ OPERATORS

Persi Diaconis, Stanford University. Understanding the eigenvalues of random matrices in the classical compact ensembles led (in joint work with Shahshahani) to showing that the joint distribution of the traces of powers have Gaussian limits (to amazing accuracy). This turns out to be equivalent to some theorems about Toeplitz operators---the strong Szegö limit theorems (work with Dan Bump). The equivalence is quite mysterious (at least to me) and linked to strange identities (cf work of Tracy-Widom-deHaye). I hope that the assembled brain power at our conference can shed some light on it.

Research problem 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).

The Institute for Advanced Study / IAS / Park City Mathematics Institute (PCMI) is designed for mathematics educators at the secondary and post-secondary level, as well as mathematics researchers and students at the post-secondary level. These groups find at PCMI an intensive mathematical experience geared to their individual needs. Moreover, the interaction among groups with different backgrounds and professional needs increases each participant’s appreciation of the mathematical community as a whole as well as the work of participants in different areas.

For more information, visit https://pcmi.ias.edu