The spectrum of asymptotic Cayley trees

Author:

Durhuus BergfinnurORCID,Jonsson ThordurORCID,Wheater JohnORCID

Abstract

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.

Funder

Villum Fonden

Publisher

IOP Publishing

Reference15 articles.

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