Cutoff on Trees is Rare

Nina Gantert (), Evita Nestoridi () and Dominik Schmid ()
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Nina Gantert: Technical University of Munich
Evita Nestoridi: Stony Brook University
Dominik Schmid: University of Bonn

Journal of Theoretical Probability, 2024, vol. 37, issue 2, 1417-1444

Abstract: Abstract We study the simple random walk on trees and give estimates on the mixing and relaxation times. Relying on a seminal result by Basu, Hermon and Peres characterizing cutoff on trees, we give geometric criteria that are easy to verify and allow to determine whether the cutoff phenomenon occurs. We provide a general characterization of families of trees with cutoff, and show how our criteria can be used to prove the absence of cutoff for several classes of trees, including spherically symmetric trees, Galton–Watson trees of a fixed height, and sequences of random trees converging to the Brownian continuum random tree.

Keywords: Random walk; Spectral gap; Mixing time; Cutoff phenomenon; 60J27; 60K37 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10959-023-01274-5

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