Mixing on $k$ Columns of the Transvection Walk
Natesh Pillai; Aaron Smith · 2026 · arXiv
WASTE classifies this as Replication Failure · AI classification, approximate
A previously reported effect did not replicate here — verify it holds before you build on it.
Abstract (excerpt)
In Diaconis and Saloff-Coste (1996), the authors introduced the simple ``transvection" walk on $\mathrm{GL}_n(\mathbb F_2)$: at each step, choose two distinct rows and add one to the other. In Ben-Hamou (2025), the author recently proved that this walk has mixing time $O(n^2\log n)$. Inspired by applications in cryptography (see Sotiraki (2016)), Ben-Hamou and Peres (2018) conjectured that the first $k$ columns of this walk mixed in $O(nk \log(n))$ steps. Our main result is a proof of this conjecture uniformly in $n$ and $k.$ Our proof is based on a local-to-global entropy estimate, in the spi
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Metadata source: arXiv