Expansions and penultimate distributions of maxima of bivariate normal random vectors

It is well known that the marginal maxima of nn standard normal random vectors with correlation coefficient ρ<1ρ<1 are asymptotically independent. In this article, the residual dependence will be captured by asymptotic expansions and certain penultimate distributions including the case where ρ(n)↑1ρ(n)↑1 at a certain rate.