Asymptotics of the major index of a random standard tableau

Pierre-Loïc Méliot; Ashkan Nikeghbali

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arXiv · 2210.13022

Asymptotics of the major index of a random standard tableau

Pierre-Loïc Méliot·Ashkan Nikeghbali

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Abstract

In this article, we establish the mod-$\phi$ convergence of the major index of a uniform random standard tableau whose shape converges in the Thoma simplex. This implies various probabilistic estimates, in particular speed of convergence estimates of Berry--Esseen type, and strong large deviation principles.

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Pierre-Loïc Méliot, Ashkan Nikeghbali. 2022-10-24. Asymptotics of the major index of a random standard tableau. https://arxiv.org/abs/2210.13022

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