ON THE NUMBER OF CYCLES IN COMMUTATORS OF RANDOM PERMUTATIONS

• 成果类型: Article
• 署名作者: Dubach, Guillaume
• 署名单位: Institut Polytechnique de Paris; Ecole Polytechnique
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/24-AAP2059
• 发表日期: 2024
• 页码: 4072-4084
• 关键词: matrix; WORD

摘要

We present general links between statistics of non-Hermitian random matrices and the distribution of the number of cycles of some specific random permutations. In particular, we derive explicit formulas for the generating functions of the number of cycles in the commutator [ sigma, tau] ] = sigma tau sigma (- 1 )tau (- 1) where sigma is uniformly distributed, and tau is either one cycle, the product of many transpositions, or the product of two cycles of same size, the latter case being a new result.