Expansions and penultimate distributions of maxima of bivariate normal random vectors

It is well known that the marginal maxima of n$n$ standard normal random vectors with correlation coefficient ρ<1$\rho <1$ 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)↑1$\rho \left(n\right)\uparrow 1$ at a certain rate.