Mock-Gaussian behaviour for linear statistics of classical compact groups

Authors: Hughes C.P.1; Rudnick Z.2

Source: Journal of Physics A: Mathematical and General, Volume 36, Number 12, 2003 , pp. 2919-2932(14)

Publisher: Institute of Physics Publishing

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Abstract:

We consider the scaling limit of linear statistics for eigenphases of a matrix taken from one of the classical compact groups. We compute their moments and find that the first few moments are Gaussian, whereas the limiting distribution is not. The precise number of Gaussian moments depends upon the particular statistic considered.

Language: English

Document Type: Miscellaneous

Affiliations: 1: American Institute of Mathematics, 360 Portage Avenue, Palo Alto, CA 94306-2244, USA 2: Raymond and Beverly Sackler School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel

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