Asymptotics of characters of symmetric groups related to Stanley character formula
Abstract
We prove an upper bound for characters of the symmetric groups. Namely, 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 |Tr \rho^\lambda(\pi) / Tr \rho^\lambda(e)| < [a max(r(\lambda)/n, c(\lambda)/n,|\pi|/n) ]^{|\pi|}, where |\pi| is the minimal number of factors needed to write \pi\in 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.
Keywords
Cite
@article{arxiv.math/0701051,
title = {Asymptotics of characters of symmetric groups related to Stanley character formula},
author = {Valentin Féray and Piotr Sniady},
journal= {arXiv preprint arXiv:math/0701051},
year = {2011}
}
Comments
Version 4: Change of title, shortened to 20 pages. Version 3: 24 pages, the title and the list of authors were changed. Version 2: 14 pages, the title, abstract and the main result were changed. Version 1: 10 pages (mistake in Lemma 7- which is false)