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.
Original language | English |
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Article number | 215202 |
Journal | Journal of Physics A: Mathematical and Theoretical |
Volume | 57 |
Issue number | 21 |
Number of pages | 24 |
ISSN | 1751-8113 |
DOIs | |
Publication status | Published - 2024 |
Bibliographical note
Publisher Copyright:
© 2024 The Author(s). Published by IOP Publishing Ltd.
- Cayley tree, graph spectrum, quantum walk, random walk
Research areas
ID: 395025384