The random k cycle walk on the symmetric group

• 成果类型: Article
• 署名作者: Hough, Bob
• 署名单位: Stanford University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-015-0636-6
• 发表日期: 2016
• 页码: 447-482
• 关键词: finite-groups; characters; bounds

摘要

We study the random walk on the symmetric group generated by the conjugacy class of cycles of length k. We show that the convergence to uniform measure of this walk has a cut-off in total variation distance after steps, uniformly in as . The analysis follows from a new asymptotic estimation of the characters of the symmetric group evaluated at cycles.