Total Variation Bound for Kac’s Random Walk
نویسنده
چکیده
We show that the classical Kac’s random walk on S starting from the point mass at e1 mixes in O(n log n) steps in total variation distance. This improves a previous bound by Diaconis and Saloff-Coste of O(n).
منابع مشابه
Convergence of Kac’s Random Walk
We study a long standing open problem on the mixing time of Kac’s random walk on SO(n,R) by random rotations. We obtain an upper bound mix = O(n log n) for the weak convergence which is close to the trivial lower bound Ω(n). This improves the upper bound O(n log n) by Diaconis and Saloff-Coste [9]. The proof is a variation on the coupling technique we develop to bound the mixing time for compac...
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