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N. Pillai

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#machine learning Preprint Aug 2026

On the Pseudo-Mixing of Kac's Walk

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 accur...

N. Pillai, Aaron Smith, Vinod Vaikuntanathan · 3 citations · ⚡1