Cutoff on trees is rare
- 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.
| Author: | Nina Gantert, Evita Nestoridi, Dominik SchmidGND |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-1231356 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/123135 |
| ISSN: | 0894-9840OPAC |
| ISSN: | 1572-9230OPAC |
| Parent Title (English): | Journal of Theoretical Probability |
| Publisher: | Springer Science and Business Media LLC |
| Place of publication: | Berlin |
| Type: | Article |
| Language: | English |
| Year of first Publication: | 2024 |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2025/06/27 |
| Volume: | 37 |
| Issue: | 2 |
| First Page: | 1417 |
| Last Page: | 1444 |
| DOI: | https://doi.org/10.1007/s10959-023-01274-5 |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Stochastik und ihre Anwendungen | |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Licence (German): |  CC-BY 4.0: Creative Commons: Namensnennung |
