@article{Dejtrakulwongse2026, 
author = {Natthapol Dejtrakulwongse and Suporn Jongpreechaharn and Kritsana Neammanee},
title = {Nonuniform Berry–Esseen bound for character ratios},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {7},
pages = {23149-23172},
keywords = {character ratio, normal approximation, uniform and nonuniform bounds, Stein's method and Jack measure},
url = {https://www.sciopen.com/article/10.3934/math.2026933},
doi = {10.3934/math.2026933},
abstract = {The first uniform bound in the normal approximation for character ratios was obtained by Fulman (2005) with the rate of convergence    O  (      n          −      1              /            4        ), and later improved to    O  (      n          −      1              /            2        ) by Shao and Su (2006). In this work, we use Stein's method and the Jack measure to derive a nonuniform Berry–Esseen-type bound for character ratios. Our result yields a sharper constant compared to previously known estimates. We also discuss an application of this approximation, particularly its role in random walk on the symmetric group        S    n  .}
}