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Asymptotic spectral analysis of growing regular graphs
Author(s):
Akihito
Hora;
Nobuaki
Obata
Journal:
Trans. Amer. Math. Soc.
360
(2008),
899-923.
MSC (2000):
Primary 46L53;
Secondary 05C50, 42C05, 60F05, 81S25
Posted:
August 29, 2007
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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:
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
Posted:
August 29, 2007
Additional Notes:
This work was supported in part by JSPS Grant-in-Aid for Scientific Research No.~15340039.
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
Forward Citation(s): Information for authors on submitting citations The following works have cited this article A. Hora and N. Obata, Quantum Probability and Spectral Analysis of Graphs, Springer, 2007.
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