math.PR · 2026-08-19 · No. 89

Probability, 2026-08-19.

1 new papers in math.PR. Titles, authors, abstracts. Links to arXiv. Want this in your inbox every morning? Subscribe →

01 — The papers

1 entries
  1. 01

    On the Pseudo-Mixing of Kac's Walk

    Natesh S. Pillai, Aaron Smith, Vinod Vaikuntanathan

    math.PR · cs.CR · cs.LG

    Motivated by a conjecture of Vaikuntanathan and Zamir, we study the pseudo-mixing of Kac's walk on $\mathrm{SO}(n)$: whether short trajectories are indistinguishable from Haar measure by low-complexity tests. We prove that the first $k$ columns mix in Wasserstein distance in $O(n(k+\log n)\log n)$ steps for fixed accuracy, resolving a conjecture of Oliveira. Combining this with a representation-theoretic variance bound, we show that if...

    arxiv.org/abs/2608.17374 · PDF

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