An Isaac Newton Institute Workshop

Recent Perspectives in Random Matrix Theory and Number Theory

Mock-Gaussian behaviour

8th April 2004

Author: C.P. Hughes (AIM)

Abstract

Mock-Gaussian behaviour is when a smooth counting function (or linear statistic) has its first few moments equal to the moments of a Gaussian distribution, even though it is not a normal distribution. In this lecture we will see that this behaviour holds eigenvalues of random matrices, and analogously for the zeros of the Riemann zeta function and other L-functions. The research presented in this lecture is joint with Zeev Rudnick.

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