The discrepancy between minmax statistics of Gaussian and Gaussiansubordinated matrices
Abstract
We compute quantitative bounds for measuring the discrepancy between the distribution of two minmax statistics involving either pairs of Gaussian random matrices, or one Gaussian and one Gaussiansubordinated random matrix. In the fully Gaussian setup, our approach allows us to recover quantitative versions of wellknown inequalities by Gordon (1985, 1987, 1992), thus generalising the quantitative version of the SudakovFernique inequality deduced in Chatterjee (2005). On the other hand, the Gaussiansubordinated 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 WienerItô integrals, that we illustrate with an example having a statistical flavour.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.12137
 Bibcode:
 2021arXiv210912137P
 Keywords:

 Mathematics  Probability