Asymptotics of the major index of a random standard tableau

2022/10/24 by Pierre‐Loïc Méliot, Méliot, Pierre-Loïc, Ashkan Nikeghbali +1
Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Probability (math.PR)

paper · doi:10.48550/arxiv.2210.13022

openalex publication_date 2022/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we establish the mod-ϕ 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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