Recent Perspectives in Random Matrix Theory and Number Theory

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Approximation of Haar distributed matrices and limiting distributions of eigenvalues of Jacobi ensembles (2009, background): “For some connections between random matrix theory and other fields of mathematics, particularly the number theory, one can see, e.g., Conrey, Farmer, Mezzadri and Snaith[18], Deift[23], Katz and Sanark [50], and Mezzardi and Snaith[55].”
Tensor Programs III: Neural Matrix Laws (2020, background): “3 Semicircle Law The Semicircle Law [45, 46] is a classical result, of central importance in statistics, physics, and engineering [8, 20, 29, 44], on the spectrum of a random Hermitian matrix with independent, zeromean entries.”
Mod-Gaussian convergence: new limit theorems in probability and number theory (2008, methodology): “[14] for recent surveys of this connection).”
A hybrid Euler-Hadamard product for the Riemann zeta function (2007, unknown): “CONJECTURE 1 (see Keating and Snaith [14] The characteristic polynomial approach has been successful in providing insight into other important and previously intractable problems in number theory as well (see, e.g., [16] for a survey of recent results).”
How to generate random matrices from the classical compact groups (2006, background): “Since there are not other symmetries in the problem, this is the only constraint that we can impose.”