Mark Rudelson (4.1) Delocalization of the eigenvectors of random matrices, part 4.1
Channel: IAS | Park City Mathematics Institute | PCMI
Date: 14/07/2017

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. 
Mark Rudelson, University of Michigan
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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