The spectrum of asymptotic Cayley trees
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We characterize the spectrum of the transition matrix for simple random walk on graphs consisting of a finite graph with a finite number of infinite Cayley trees attached. We show that there is a continuous spectrum identical to that for a Cayley tree and, in general, a non-empty pure point spectrum. We apply our results to studying continuous time quantum walk on these graphs. If the pure point spectrum is nonempty the walk is in general confined with a nonzero probability.
Originalsprog | Engelsk |
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Artikelnummer | 215202 |
Tidsskrift | Journal of Physics A: Mathematical and Theoretical |
Vol/bind | 57 |
Udgave nummer | 21 |
Antal sider | 24 |
ISSN | 1751-8113 |
DOI | |
Status | Udgivet - 2024 |
Bibliografisk note
Funding Information:
JFW\u2019s research was funded by Research England. B D acknowledges support from Villum Fonden via the QMATH Centre of Excellence (Grant No. 10059). T J would like to acknowledge hospitality at the Rudolf Peierls Centre for Theoretical Physics in Oxford and at the Department of Mathematical Sciences in the University of Copenhagen.
Publisher Copyright:
© 2024 The Author(s). Published by IOP Publishing Ltd.
ID: 395025384