Comparison inequalities for order statistics of Gaussian arrays

Normal comparison lemma and Slepian’s inequality are essential tools for the analysis of extremes of Gaussian processes. In this paper we show that the Normal comparison lemma for Gaussian vectors can be extended to order statistics of Gaussian arrays. Our applications include the derivation of mixed Gumbel limit laws for the order statistics of stationary Gaussian processes and the investigation of lower tail behavior of order statistics of self-similar Gaussian processes.