The discrepancy between min-max statistics of Gaussian and Gaussian-subordinated matrices

Giovanni Peccati; Nicola Turchi

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arXiv · 2109.12137

The discrepancy between min-max statistics of Gaussian and Gaussian-subordinated matrices

Giovanni Peccati·Nicola Turchi

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Abstract

We compute quantitative bounds for measuring the discrepancy between the distribution of two min-max statistics involving either pairs of Gaussian random matrices, or one Gaussian and one Gaussian-subordinated random matrix. In the fully Gaussian setup, our approach allows us to recover quantitative versions of well-known inequalities by Gordon (1985, 1987, 1992), thus generalising the quantitative version of the Sudakov-Fernique inequality deduced in Chatterjee (2005). On the other hand, the Gaussian-subordinated case yields generalizations of estimates by Chernozhukov et al. (2015) and Koike (2019). As an application, we establish fourth moment bounds for matrices of multiple stochastic Wiener-It\^o integrals, that we illustrate with an example having a statistical flavour.

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Giovanni Peccati, Nicola Turchi. 2021-09-24. The discrepancy between min-max statistics of Gaussian and Gaussian-subordinated matrices. https://arxiv.org/abs/2109.12137

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