## Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

## If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

# The Berry-Esseen Bound for Character Ratios

Qi-Man Shao and Zhong-Gen Su
Proceedings of the American Mathematical Society
Vol. 134, No. 7 (Jul., 2006), pp. 2153-2159
Stable URL: http://www.jstor.org/stable/4098248
Page Count: 7
Preview not available

## Abstract

Let λ be a partition of n chosen from the Plancherel measure of the symmetric group Sn, let $\chi^{\lambda}(12)$ be the irreducible character of the symmetric group parameterized by λ evaluated on the transposition (12), and let $dim(\lambda)$ be the dimension of the irreducible representation parameterized by λ. Fulman recently obtained the convergence rate O(n-s) for any $0 < s < \frac{1}{2}$ in the central limit theorem for character ratios $\frac{(n-1)}{\sqrt{2}} \frac{\xi^{\lambda} (12)}{\dim (\lambda)}$ by developing a connection between martingale and character ratios, and he conjectures that the correct speed is O(n-1/2). In this paper we confirm the conjecture via a refinement of Stein's method for exchangeable pairs.

• 2153
• 2154
• 2155
• 2156
• 2157
• 2158
• 2159