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Mock-Gaussian behavior in the classical compact groups and number theory

Mathematical Physics & Probability

Speaker: Dr. Chris Hughes, American Institute of Mathematics
Location: 493 Kerr
Start time: Tue, Nov 26 2002, 3:10PM

We will study the distribution of a linear statistic of critically scaled eigenphases of a matrix taken at random from one of classical compact groups. The first few moments are found to be Gaussian, whereas the distribution of the linear statistic is not Gaussian. A similar phenomenon is found for the smooth counting function of low-lying zeroes of L-functions.