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The discrepancy in min-max statistics between two random matrices with finite third moments
Zijun Chen, Yiming Chen, Chengfu Wei · 2024-11-13 · via math.PR updates on arXiv.org

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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