Stein’s method and Plancherel measure of the symmetric group
نویسندگان
چکیده
منابع مشابه
Stein's Method and Plancherel Measure of the Symmetric Group Running Head: Stein's Method and Plancherel Measure
X iv :m at h/ 03 05 42 3v 3 [ m at h. R T ] 1 1 N ov 2 00 3 Stein’s Method and Plancherel Measure of the Symmetric Group Running head: Stein’s Method and Plancherel Measure By Jason Fulman University of Pittsburgh Department of Mathematics 301 Thackeray Hall Pittsburgh, PA 15260 Email: [email protected] Abstract: We initiate a Stein’s method approach to the study of the Plancherel measure of...
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We initiate a Stein’s method approach to the study of the Plancherel measure of the symmetric group. A new proof of Kerov’s central limit theorem for character ratios of random representations of the symmetric group on transpositions is obtained; the proof gives an error term. The construction of an exchangeable pair needed for applying Stein’s method arises from the theory of harmonic function...
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1.1. Plancherel measures. Given a finite group G, by the corresponding Plancherel measure we mean the probability measure on the set G∧ of irreducible representations of G which assigns to a representation π ∈ G∧ the weight (dim π)/|G|. For the symmetric group S(n), the set S(n)∧ is the set of partitions λ of the number n, which we shall identify with Young diagrams with n squares throughout th...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2004
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-04-03499-3