EVENT DETAILS AND ABSTRACT

Title: The empirical spectral distribution (ESD) of a deterministic matrix plus small random noise.
Speaker: Philip M. Wood
Speaker Info: University of Wisconsin
Brief Description:
Special Note:
Abstract:

A deterministic n by n matrix has a distribution of eigenvalues in the complex plane. Small random noise can be formed by a random n by n matrix with independent, identically distributed mean 0 variance 1 entries scaled by n^(-gamma) for gamma > 1/2, which by itself has eigenvalues collapsing to the origin. What happens to the eigenvalues of the deterministic matrix when you add a small random noise matrix? There are interesting cases where the eigenvalue distribution is known to change dramatically when small Gaussian random noise is added, and this talk will focus on what happens when the noise is not Gaussian.