Oren, Idan, Godel, Amit and Smilansky, Uzy 2009. Trace formulae and spectral statistics for discrete Laplacians on regular graphs (I). Journal of Physics A: Mathematical and Theoretical 42 (41) , 415101. 10.1088/1751-8113/42/41/415101 |
Abstract
Trace formulae for d-regular graphs are derived and used to express the spectral density in terms of the periodic walks on the graphs under consideration. The trace formulae depend on a parameter w which can be tuned continuously to assign different weights to different periodic orbit contributions. At the special value w = 1, the only periodic orbits which contribute are the non-back-scattering orbits, and the smooth part in the trace formula coincides with the Kesten–McKay expression. As w deviates from unity, non-vanishing weights are assigned to the periodic walks with backscatter, and the smooth part is modified in a consistent way. The trace formulae presented here are the tools to be used in the second paper in this sequence, for showing the connection between the spectral properties of d-regular graphs and the theory of random matrices.
Item Type: | Article |
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Date Type: | Publication |
Status: | Published |
Schools: | 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/15159 |
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