Probability Seminar | Sidhanth Mohanty (Northwestern)

Title: Eigenvalue bounds for random matrices via zerofreeness

Abstract: A central theme in random matrix theory is to understand the spectral radius of a random matrix.  We introduce a new technique to bound the spectral radius of a random technique based on a complex analytic formula to count zeros of an analytic function.

Our technique yields new and simpler proofs of spectral radius bounds that are sharp up to a constant for many random matrix ensembles, notably a random matrix with independent entries, a symmetric random matrix with independent entries, and the adjacency matrix of a random d-regular graph.

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