PreprintCC BY 4.0arXiv
Cutoff on non-negatively curved chains without symmetric support condition
Abstract
We establish a cutoff criterion for finite Markov chains with non-negative Bakry--Émery curvature without assuming that the support of the transition matrix is symmetric. This extends a criterion of Salez based on a refined product condition. For each allowed transition, we consider a shortest directed path from its endpoint back to its starting point. Our cutoff criterion depends on the maximum length of these paths. We also obtain a discrete-time counterpart for lazy chains. For random walks on finite Abelian groups, we prove non-negative Bakry--Émery curvature for arbitrary generating sets. As an application, we establish almost-sure cutoff for random walks on products of cyclic groups of order three.
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BibTeX
@misc{okamura2026cutoff,
title = {{Cutoff on non-negatively curved chains without symmetric support condition}},
author = {Kazuki Okamura},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28518},
eprint = {2609.28518},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28518},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Cutoff on non-negatively curved chains without symmetric support condition
AU - Kazuki Okamura
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.28518
UR - https://arxiv.org/abs/2609.28518
AB - We establish a cutoff criterion for finite Markov chains with non-negative Bakry--Émery curvature without assuming that the support of the transition matrix is symmetric. This extends a criterion of Salez based on a refined product condition. For each allowed transition, we consider a shortest directed path from its endpoint back to its starting point. Our cutoff criterion depends on the maximum length of these paths. We also obtain a discrete-time counterpart for lazy chains. For random walks on finite Abelian groups, we prove non-negative Bakry--Émery curvature for arbitrary generating sets. As an application, we establish almost-sure cutoff for random walks on products of cyclic groups of order three.
ER -