Random Matrices Learning Seminar

Daniel Perales Anaya, Pure Math Department, University of Waterloo

"Random matrices, interlacing families of polynomials, and the expected characteristic polynomial"

In this session we will continue with the proof of the conjecturedue to Bilu and Linial concerning with bounding the maximumeigenvalue of +/- signings of edges of a d-regular graph.In particular, we are going to focus on the proof of the Theoremthat provides us with a huge family of real rooted polynomialsthat came from a convex combination of certain polynomials.To achieve this we will study the concept of real stability,which is a generalization to multivariable polynomials of the concept of being real rooted.

MC 5403