The Spectrum of Asymptotic Cayley Trees

• URL: http://arxiv.org/abs/2312.09833v2
• Date: Mon, 15 Apr 2024 14:44:01 GMT
• Title: The Spectrum of Asymptotic Cayley Trees
• Abstract summary: We show that there is a continuous spectrum identical to that for a Cayley tree and, in general, a non-empty pure point spectrum. If the pure point spectrum is nonempty the walk is in general confined with a nonzero probability.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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