Diane Holcomb: Random matrices via differential equations

Speaker: Diane Holcomb

Title: Random matrices via differential equations

Abstract: Random matrices started with the work of Wishart (1920s) and Wigner (1950s). They introduced random matrix models that were used to model certain behavior. For Wishart this was the behavior of a "typical" covariance matrix, and for Wigner the eigenvalues modeled the electron spacing of a heavy atom.

In this talk we will focus on the local interactions of the eigenvalues. These can be seen if we rescale the spectrum so that the spacing between eigenvalues remains order 1 as the size of the matrix tends to infinity.

We will focus on describing these limiting processes via differential equations.