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.
Evita Nestoridi has been funded by EP/R022615/1. Oanh Nguyen has been funded by NSF grant DMS-1954174.
We thank the anonymous referee for their helpful comments.
"The full spectrum of random walks on complete finite d-ary trees." Electron. J. Probab. 26 1 - 17, 2021. https://doi.org/10.1214/21-EJP608