Asymptotics of characters of symmetric groups related to Stanley character formula

• 成果类型: Article
• 署名作者: Feray, Valentin; Sniady, Piotr
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2011.173.2.6
• 发表日期: 2011
• 页码: 887-906
• 关键词: representations

摘要

We prove an upper bound for characters of the symmetric groups. In particular, we show that there exists a constant a > 0 with a property that for every Young diagram lambda with n boxes, r(lambda) rows and c(lambda) columns vertical bar Tr rho(lambda)(pi)/Tr rho(lambda)(e)vertical bar <= [a max (r(lambda)/n, c(lambda)/n, vertical bar pi vertical bar/n)](vertical bar pi vertical bar), where vertical bar pi vertical bar is the minimal number of factors needed to write pi is an element of S-n as a product of transpositions. We also give uniform estimates for the error term in the Vershik-Kerov's and Biane's character formulas and give a new formula for free cumulants of the transition measure.