Maxima of a triangular array of multivariate Gaussian sequence

It is known that the normalized maxima of a sequence of independent and identically distributed bivariate normal random vectors with correlation coefficient $\rho \in (-1,1)$ is asymptotically independent, which may seriously underestimate extreme probabilities in practice. By letting $\rho$ depend on the sample size and go to one with certain rate, H\"usler and Reiss (1989) showed that the normalized maxima can become asymptotically dependent. In this paper, we extend such a study to a triangular array of multivariate Gaussian sequence, which further generalizes the results in Hsing, H\"usler and Reiss (1996) and Hashorva and Weng (2013).