Open Access
2022 No cutoff in Spherically symmetric trees
Rafael Chiclana, Yuval Peres
Author Affiliations +
Electron. Commun. Probab. 27: 1-11 (2022). DOI: 10.1214/22-ECP468

Abstract

We show that for lazy simple random walks on finite spherically symmetric trees, the ratio of the mixing time and the relaxation time is bounded by a universal constant. Consequently, lazy simple random walks on any sequence of finite spherically symmetric trees do not exhibit pre-cutoff; this conclusion also holds for continuous-time simple random walks. This answers a question recently proposed by Gantert, Nestoridi, and Schmid. We also show that for lazy simple random walks on finite spherically symmetric trees, hitting times of vertices are (uniformly) non concentrated. Finally, we study the stability of our results under rough isometries.

Citation

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Rafael Chiclana. Yuval Peres. "No cutoff in Spherically symmetric trees." Electron. Commun. Probab. 27 1 - 11, 2022. https://doi.org/10.1214/22-ECP468

Information

Received: 16 September 2021; Accepted: 16 April 2022; Published: 2022
First available in Project Euclid: 10 May 2022

MathSciNet: MR4424033
zbMATH: 1489.05129
arXiv: 2107.14111
Digital Object Identifier: 10.1214/22-ECP468

Subjects:
Primary: 05C05 , 05C81 , 60J10

Keywords: Cutoff , Markov chains , mixing time , Random walks , tree

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