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Simons Foundation

Beyond Gaussians emerging from independence, for many correlated systems, new types of universal distributions have emerged in the past sixty years, which appear to effectively describe a wide range of statistical physics phenomena. Surprisingly, numerical and theoretical evidence has shown that these new, intricate statistics also reflect several aspects of the distribution of prime numbers, and of arithmetic objects in general. This question is relevant for all arithmetic topics covered in this meeting: conjectures from random matrix theory, distributions of multiplicative functions, limit theorems for L-functions, and the anatomy of integers.

American Statistical Association (ASA)