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The limiting spectral law of sparse iid matrices

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OOEW04 - Structure and Randomness - a celebration of the mathematics of Timothy Gowers

Let A be an n by n matrix where each entry is independent and takes 1 with probability p, and 0 otherwise. In this talk we will be interested in the general “shape” that the distribution of eigenvalues of A has in the complex plane. While the study of these distributions goes back to the work of Wigner in the 1950s, many basic questions are still not understood. Indeed, for small p, it is not even known if this limiting “shape” converges to a deterministic distribution as n tends to infinity. Here I will discuss the recent resolution of this problem. Based on joint work Ashwin Sah and Mehtaab Sawhney.

This talk is part of the Isaac Newton Institute Seminar Series series.

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