The Berry-esseen Bound for Character Ratios
نویسندگان
چکیده
Let λ be a partition of n chosen from the Plancherel measure of the symmetric group Sn, let χλ(12) be the irreducible character of the symmetric group parameterized by λ evaluated on the transposition (12), and let dim(λ) be the dimension of the irreducible representation parameterized by λ. Fulman recently obtained the convergence rate of O(n−s) for any 0 < s < 1 2 in the central limit theorem for character ratios (n−1) √ 2 χ(12) dim(λ) 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.
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