On the spectrum of random walks on complete finite $d$-ary trees

Evita Nestoridi; Oanh Nguyen

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arXiv · 1912.06771

On the spectrum of random walks on complete finite $d$-ary trees

Evita Nestoridi·Oanh Nguyen

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Abstract

In the present paper, we determine the full spectrum of the simple random walk on finite, complete $d$-ary trees. We also find an eigenbasis for the transition matrix. As an application, we apply our results to get a lower bound for the interchange process on complete, finite d-ary trees, which we conjecture to be sharp.

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Evita Nestoridi, Oanh Nguyen. 2019-12-14. On the spectrum of random walks on complete finite $d$-ary trees. https://arxiv.org/abs/1912.06771

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