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                * Princeton Discrete Math Seminar *
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Speaker: Mehtaab Sawhney (MIT)

Thursday 26th October, 3:00 in Fine Hall 224.

Title: The limiting spectral distribution of iid matrices

Let A be an n by n matrix with iid Ber(d/n) entries. We show that the
empirical measure of the eigenvalues converges, in probability, to a
deterministic distribution. The proof involves incrementally exposing the
randomness of the underlying matrix and studying the evolution of the singular
values. Another component of the proof relies on understanding the structure of
near singular vectors via expansion of the underlying bipartite graph. The talk
will focus on the simpler model case where we give a substantially simplified
proof of the sparse circular law of Rudelson and Tikhomirov. 
Joint with Ashwin Sah and Julian Sahasrabudhe.

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