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The limit distribution of maxima formed by a triangular array of independent and identically distributed bivariate Gaussian random vectors is the Hüsler-Reiss max-stable distribution if and only if the correlation of each vector approaches one with a certain rate. In this paper, we introduce a second-order condition on the convergence rate of this correlation. Under this condition we derive the uniform convergence rate of the distribution of normalized bivariate maxima to its ultimate limit distribution.

Convergence rate of maxima of bivariate Gaussian arrays to the Hüsler-Reiss distribution