TOTAL VARIATION BOUND FOR KAC'S RANDOM WALK

• 成果类型: Article
• 署名作者: Jiang, Yunjiang
• 署名单位: Stanford University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/11-AAP810
• 发表日期: 2012
• 页码: 1712-1727
• 关键词: master equation; spectral gap; MODEL

摘要

We show that the classical Kac's random walk on (n - 1)-sphere Sn-1 starting from the point mass at e(1) mixes in O(n(5)(log n)(3)) steps in total variation distance. The main argument uses a truncation of the running density after a burn-in period, followed by L-2 convergence using the spectral gap information derived by other authors. This improves upon a previous bound by Diaconis and Saloff-Coste of order O(n(2n)).