Convergence of Kac’s Random Walk
نویسندگان
چکیده
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 compact Markov chains, which is of independent interest.
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تاریخ انتشار 2007