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August 2012 Total variation bound for Kac’s random walk
Yunjiang Jiang
Ann. Appl. Probab. 22(4): 1712-1727 (August 2012). DOI: 10.1214/11-AAP810

Abstract

We show that the classical Kac’s random walk on (n1)-sphere Sn1 starting from the point mass at e1 mixes in O(n5(logn)3) steps in total variation distance. The main argument uses a truncation of the running density after a burn-in period, followed by L2 convergence using the spectral gap information derived by other authors. This improves upon a previous bound by Diaconis and Saloff-Coste of order O(n2n).

Citation

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Yunjiang Jiang. "Total variation bound for Kac’s random walk." Ann. Appl. Probab. 22 (4) 1712 - 1727, August 2012. https://doi.org/10.1214/11-AAP810

Information

Published: August 2012
First available in Project Euclid: 10 August 2012

zbMATH: 1248.60004
MathSciNet: MR2985175
Digital Object Identifier: 10.1214/11-AAP810

Subjects:
Primary: 60-XX

Keywords: interacting particle systems , Kac random walk , Markov chain mixing time , orthogonal group

Rights: Copyright © 2012 Institute of Mathematical Statistics

Vol.22 • No. 4 • August 2012
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