The spectrum of asymptotic Cayley trees
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...
| Hlavní autoři: | , , |
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| Médium: | Journal article |
| Jazyk: | English |
| Vydáno: |
IOP Publishing
2024
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| _version_ | 1826313361473667072 |
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| author | Durhuus, B Jonsson, T Wheater, J |
| author_facet | Durhuus, B Jonsson, T Wheater, J |
| author_sort | Durhuus, B |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-09-25T04:11:55Z |
| format | Journal article |
| id | oxford-uuid:457f8e5c-9e5d-49af-8d6a-5b55a3ffb2c8 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-09-25T04:11:55Z |
| publishDate | 2024 |
| publisher | IOP Publishing |
| record_format | dspace |
| spelling | oxford-uuid:457f8e5c-9e5d-49af-8d6a-5b55a3ffb2c82024-07-02T08:17:14ZThe spectrum of asymptotic Cayley treesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:457f8e5c-9e5d-49af-8d6a-5b55a3ffb2c8EnglishSymplectic ElementsIOP Publishing2024Durhuus, BJonsson, TWheater, JWe 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. |
| spellingShingle | Durhuus, B Jonsson, T Wheater, J The spectrum of asymptotic Cayley trees |
| title | The spectrum of asymptotic Cayley trees |
| title_full | The spectrum of asymptotic Cayley trees |
| title_fullStr | The spectrum of asymptotic Cayley trees |
| title_full_unstemmed | The spectrum of asymptotic Cayley trees |
| title_short | The spectrum of asymptotic Cayley trees |
| title_sort | spectrum of asymptotic cayley trees |
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