Mark Rudelson (1.2) Delocalization of the eigenvectors of random matrices, part 1.2
Channel: IAS | Park City Mathematics Institute | PCMI
Date: 10/07/2017

Lecture notes can be found at https://pcmi.ias.edu/sites/pcmi.ias.edu/files/Mark%20Rudelson%20Lecture%20Notes.pdf

Consider a random matrix with i.i.d. normal entries. Since its distribution is invariant under rotations, any normalized eigenvector is uniformly distributed over the unit sphere. For a general distribution of the entries, this is no longer true. Yet, if the size of the matrix is large, the eigenvectors are distributed approximately uniformly. This property, called delocalization, can quantified in various senses. In these lectures, we will discuss recent results on delocalization for general random matrices

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