Activities[ Edit ]
Advisor: Ron Rosenthal
Abstract: A random matrix is said to be sampled from the Ginibre ensemble if all of its entries are i.i.d., complex normal random variables with mean zero. In this work, we study the asymptotic behavior of the angles between pairs of eigenvectors of such matrices. In particular, we compute the limiting distribution of the angle for fixed pairs of eigenvalues, obtain precise bounds on the typical behavior of the maximal angle with high probability and find the limiting distribution for the location of the eigenvalues which attain the maximal angle with high probability. The talk will present the main results and demonstrate some of the techniques used to reach them.