English

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

Probability 2019-12-17 v1 Combinatorics

Abstract

In the present paper, we determine the full spectrum of the simple random walk on finite, complete dd-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.

Keywords

Cite

@article{arxiv.1912.06771,
  title  = {On the spectrum of random walks on complete finite $d$-ary trees},
  author = {Evita Nestoridi and Oanh Nguyen},
  journal= {arXiv preprint arXiv:1912.06771},
  year   = {2019}
}