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In this 40-minute conference talk, Ella Hiesmayr from UMPA ENS Lyon presents research on spectral large deviations of sparse random matrices at IPAM's Free Entropy Theory and Random Matrices Workshop. Explore the adjacency matrix of Erdos-Rényi graphs with constant average degree and i.i.d. edge weights, focusing on determining large deviations of the largest eigenvalue and examining how different weight distributions affect outcomes. Discover the surprising finding that the rate function is universal in light-tailed cases but depends on precise entry distribution in heavy-tailed scenarios, presented as a variational problem. Learn how the analysis relies on precise examination of graph geometry, as more general methods fail in sparse conditions. Recorded February 27, 2025, at the Institute for Pure & Applied Mathematics (IPAM) at UCLA.
