The discrepancy in min-max statistics between two random matrices with finite third moments

2024/11/13 by Zijun Chen, Yiming Chen, Chen, Zijun +2
Decision Sciences · #60B20 #60E15 #FOS: Mathematics #G.3 #Probability (math.PR) #Probability and Risk Models

paper · pdf · doi:10.48550/arxiv.2411.08303

openalex publication_date 2024/11/13 · openalex created_date 2024/11/16 · openalex updated_date 2026/07/28

Abstract

We propose a novel coupling inequality of the min-max type for two random matrices with finite absolute third moments, which generalizes the quantitative versions of the well-known inequalities by Gordon. Previous results have calculated the quantitative bounds for pairs of Gaussian random matrices. Through integrating the methods utilized by Chatterjee-Meckes and Reinert-Röllin in adapting Stein's method of exchangeable pairs for multivariate normal approximation, this study eliminates the Gaussian restriction on random matrices, enabling us to achieve more extensive results.

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