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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Asymptotic spectral analysis of growing regular graphs


Authors: Akihito Hora and Nobuaki Obata
Journal: Trans. Amer. Math. Soc. 360 (2008), 899-923
MSC (2000): Primary 46L53; Secondary 05C50, 42C05, 60F05, 81S25
Published electronically: August 29, 2007
MathSciNet review: 2346476
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Abstract: We propose the quantum probabilistic techniques to obtain the asymptotic spectral distribution of the adjacency matrix of a growing regular graph. We prove the quantum central limit theorem for the adjacency matrix of a growing regular graph in the vacuum and deformed vacuum states. The condition for the growth is described in terms of simple statistics arising from the stratification of the graph. The asymptotic spectral distribution of the adjacency matrix is obtained from the classical reduction.


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Additional Information

Akihito Hora
Affiliation: Graduate School of Natural Science and Technology, Okayama University, Okayama, 700-8530 Japan
Address at time of publication: Graduate School of Mathematics, Nagoya University, Nagoya, 464-8602 Japan
Email: hora@ems.okayama-u.ac.jp, hora@math.nagoya-u.ac.jp

Nobuaki Obata
Affiliation: Graduate School of Information Sciences, Tohoku University, Sendai, 980-8579 Japan
Email: obata@math.is.tohoku.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9947-07-04232-8
PII: S 0002-9947(07)04232-8
Keywords: Adjacency matrix, interacting Fock space, orthogonal polynomial, quantum central limit theorem, quantum decomposition, spectral distribution
Received by editor(s): October 17, 2005
Received by editor(s) in revised form: November 5, 2005
Published electronically: August 29, 2007
Additional Notes: This work was supported in part by JSPS Grant-in-Aid for Scientific Research No. 15340039.
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.