@article{c3e530f6e7624227aa5d267cab62824b,
title = "The full spectrum of random walks on complete finite d-ary trees",
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.",
keywords = "Random walk, Regular trees, Spectrum",
author = "Evita Nestoridi and Nguyen, {Oanh Thi Hoang}",
note = "Funding Information: *Evita Nestoridi has been funded by EP/R022615/1. Oanh Nguyen has been funded by NSF grant DMS-1954174. †Department of Mathematics, Princeton University, USA. E-mail: exn@princeton.edu ‡Department of Mathematics, Princeton University and Department of Mathematics, University of Illinois at Urbana – Champaign, USA. E-mail: onguyen@illinois.edu Publisher Copyright: {\textcopyright} 2021, Institute of Mathematical Statistics. All rights reserved.",
year = "2021",
doi = "10.1214/21-EJP608",
language = "English (US)",
volume = "26",
journal = "Electronic Journal of Probability",
issn = "1083-6489",
publisher = "Institute of Mathematical Statistics",
}