Aaron Smith

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20242026

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math.PR2026

Mixing on $k$ Columns of the Transvection Walk

Natesh Pillai, Aaron Smith

In Diaconis and Saloff-Coste (1996), the authors introduced the simple ``transvection" walk on $GL_{n} (F_{2})$ : at each step, choose two distinct rows and add one to t…

math.PR2026

Kac's walk on rotation matrices mixes in $n^{2} lo g n$ steps

Natesh S. Pillai, Aaron Smith

Kac's walk on the rotation group, introduced by Hastings in 1970, is an important high-dimensional Markov chain with applications in statistical physics, statistics, cryptography,…

Mixing on k Columns of the Transvection Walk

Kac's walk on rotation matrices mixes in n2logn steps

Mixing on $k$ Columns of the Transvection Walk

Kac's walk on rotation matrices mixes in $n^{2} lo g n$ steps