Trace formulae and spectral statistics for discrete Laplacians on regular graphs (II)

Oren, Idan and Smilansky, Uzy 2010. Trace formulae and spectral statistics for discrete Laplacians on regular graphs (II). Journal of Physics A: Mathematical and Theoretical 43 (22) , 225205. 10.1088/1751-8113/43/22/225205

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Abstract

Following the derivation of the trace formulas in the first paper in this series, we establish here a connection between the spectral statistics of random regular graphs and the predictions of random matrix theory (RMT). This follows from the known Poisson distribution of cycle counts in regular graphs, in the limit that the cycle periods are kept constant and the number of vertices increases indefinitely. The result is analogous to the so-called diagonal approximation in quantum chaos. We also show that by assuming that the spectral correlations are given by RMT to all orders, we can compute the leading deviations from the Poisson distribution for cycle counts. We provide numerical evidence which supports this conjecture.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	IOP Publishing
ISSN:	1751-8121
Last Modified:	19 Mar 2016 22:24
URI:	https://orca.cardiff.ac.uk/id/eprint/15160

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