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The spectrum of some nonlinear random matrices
February 9, 2024 @ 12:00 pm - 1:00 pm
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.