Abstract
In this paper, we obtain uniform and non-uniform bounds on the Kolmogorov distance in the normal approximation for Jack deformations of the character ratio, by using Stein’s method and zero-bias couplings. Our uniform bound comes very close to that conjectured by Fulman (J. Combin. Theory Ser. A 108 (2004) 275–296). As a by-product of the proof of the non-uniform bound, we obtain a Rosenthal-type inequality for zero-bias couplings.
Citation
Louis H.Y. Chen. Martin Raič. Lê Vǎn Thành. "On the error bound in the normal approximation for Jack measures." Bernoulli 27 (1) 442 - 468, February 2021. https://doi.org/10.3150/20-BEJ1245
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