Year: 2026
Type: preprint
Abstract: We consider a Markov chain on $\mathrm{SL}_n(\mathbb{Z}_p)$, the space of $n \times n$ matrices with determinant $1$ and entries in $\mathbb{Z}_p$, 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 $O(n^2p^2(\log n +\log \log p))$.
Source: arXiv (Cornell University)
Authors: Ben-Hamou, Anna, Overgaard, Simon
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223032358