PreprintCC BY 4.0arXiv
Mixing time of the tranvection walk on SLn(ℤp)
Abstract
We consider a Markov chain on SLn(ℤp), the space of n × n matrices with determinant $1$ and entries in ℤp, for p a prime number. At every time step, the chain updates by adding one row (or its negation) to another. By way of a log-Sobolev inequality, we show the mixing time of this chain is at most of order O(n2p2(log n +log log p)).
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BibTeX
@misc{benhamou2026mixing,
title = {{Mixing time of the tranvection walk on $\mathrmSL_n(\mathbbZ_p)$}},
author = {Anna Ben-Hamou and Simon Overgaard},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25449},
eprint = {2610.25449},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25449},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Mixing time of the tranvection walk on SL_n(ℤ_p)
AU - Anna Ben-Hamou
AU - Simon Overgaard
PY - 2026
DA - 2026/10/18
PB - arXiv
DO - 10.48550/arxiv.2610.25449
UR - https://arxiv.org/abs/2610.25449
AB - We consider a Markov chain on SL_n(ℤ_p), the space of n × n matrices with determinant $1$ and entries in ℤ_p, for p a prime number. At every time step, the chain updates by adding one row (or its negation) to another. By way of a log-Sobolev inequality, we show the mixing time of this chain is at most of order O(n^2p^2(log n +log log p)).
ER -