Total Variation Mixing Time of Kac's Random Walk

Details Total Variation Mixing Time of Kac's Random Walk Total Variation Mixing Time of Kac's Random Walk

2009-05-11

arxiv.org/abs/0905.1539v3

Mathematics

Probability

15 pages

Scientific paper

We show that the classical Kac's random walk on $S^{n-1}$ starting from the
point mass at $e_1$ mixes in $\mathcal{O}(n^5 \log n)$ steps in total variation
distance. This improves a previous bound by Diaconis and Saloff-Coste of
$\mathcal{O}(n^{2n})$.

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