CMSA Member Seminar

Speaker: Benjamin McKenna (Harvard)

Title: The spectrum of some nonlinear random matrices

Abstract: Modern data science often requires one to consider “nonlinear random matrices,” a broad term for random-matrix models whose construction involves a nonlinear function applied entrywise. Such models are typically far from classical random matrix theory, and in principle entrywise nonlinearities can affect the eigenvalues in a complicated way. However, recent years have seen a number of results on nonlinear models whose spectrum is surprisingly simple. We give one such result, emphasizing general random-matrix techniques like free probability and orthogonal polynomials. Joint work with Sofiia Dubova, Yue M. Lu, and Horng-Tzer Yau.