We establish sharp tail asymptotics for component-wise extreme values of bivariate Gaussian random vectors with arbitrary correlation between the components. We consider two scaling regimes for the tail event in which we demonstrate the existence of a restricted large deviations principle, and identify the unique rate function associated with these asymptotics. Our results identify when the maxima of both coordinates are typically attained by two different vs. the same index, and how this depends on the correlation between the coordinates of the bivariate Gaussian random vectors. Our results complement a growing body of work on the extremes of Gaussian processes. The results are also relevant for steady-state performance and simulation analysis of networks of infinite server queues.

中文翻译：

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二元高斯极值的大偏差

我们为分量之间具有任意相关性的二元高斯随机向量的分量极值建立了尖尾渐近线。我们考虑尾部事件的两种缩放方式，其中我们证明了受限大偏差原理的存在，并确定与这些渐近性相关的唯一速率函数。我们的结果确定了两个坐标的最大值何时通常由两个不同的指标与相同的指标获得，以及这如何取决于双变量高斯随机向量的坐标之间的相关性。我们的结果补充了越来越多的关于高斯过程极端的工作。结果也与无限服务器队列网络的稳态性能和仿真分析相关。