Delocalization of eigenvectors of random matrices. Lecture notes

Understand

Let $x \in S^{n-1}$ be a unit eigenvector of an $n \times n$ random matrix.

• This vector is delocalized if it is distributed roughly uniformly over the real or complex sphere.
• This intuitive notion can be quantified in various ways.
• In these lectures, we will concentrate on the no-gaps delocalization.