The BerryEsseen bound for character ratios
Authors:
QiMan Shao and ZhongGen Su
Journal:
Proc. Amer. Math. Soc. 134 (2006), 21532159
MSC (2000):
Primary 60F05; Secondary 05E10, 60C05
Published electronically:
December 19, 2005
MathSciNet review:
2215787
Fulltext PDF Free Access
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Abstract: Let be a partition of chosen from the Plancherel measure of the symmetric group , let be the irreducible character of the symmetric group parameterized by evaluated on the transposition , and let be the dimension of the irreducible representation parameterized by . Fulman recently obtained the convergence rate of for any in the central limit theorem for character ratios by developing a connection between martingale and character ratios, and he conjectures that the correct speed is . In this paper we confirm the conjecture via a refinement of Stein's method for exchangeable pairs.
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Additional Information
QiMan Shao
Affiliation:
Department of Mathematics, University of Oregon, Eugene, Oregon 97403 – and – Department of Mathematics, Department of Statistics and Applied Probability, National University of Singapore
Email:
qmshao@darkwing.uoregon.edu
ZhongGen Su
Affiliation:
Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang 310027, People’s Republic of China
DOI:
http://dx.doi.org/10.1090/S0002993905081773
PII:
S 00029939(05)081773
Keywords:
BerryEsseen bound,
character ratio,
Plancherel measure,
Stein's method.
Received by editor(s):
September 28, 2004
Received by editor(s) in revised form:
February 4, 2005
Published electronically:
December 19, 2005
Additional Notes:
The first author was supported in part by Grant R1555000035112 at the National University of Singapore
The second author was supported in part by NFS of China (No. 10371109)
Communicated by:
Richard C. Bradley
Article copyright:
© Copyright 2005
American Mathematical Society
