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...
| Những tác giả chính: | , , |
|---|---|
| Định dạng: | Journal article |
| Ngôn ngữ: | English |
| Được phát hành: |
IOP Publishing
2024
|
| Tóm tắt: | 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. |
|---|