Recently in Gao and Stoev (2020) it was established that the concentration of maxima phenomenon is the key to solving the exact sparse support recovery problem in high dimensions. This phenomenon, known also as relative stability, has been little studied in the context of dependence. Here, we obtain bounds on the rate of concentration of maxima in Gaussian triangular arrays. These results are used to establish sufficient conditions for the uniform relative stability of functions of Gaussian arrays, leading to new models that exhibit phase transitions in the exact support recovery problem. Finally, the optimal rate of concentration for Gaussian arrays is studied under general assumptions implied by the classic condition of Berman (1964).

最近，在Gao和Stoev（2020）中，已经确定最大现象的集中是解决高维精确的稀疏支护恢复问题的关键。这种现象，也称为相对稳定性，在依赖的上下文中很少研究。在这里，我们获得了高斯三角阵列中最大值集中率的界限。这些结果被用来为高斯阵列函数的统一相对稳定性建立充分的条件，从而导致新的模型在精确的支撑物恢复问题中表现出相变。最后，在Berman（1964）经典条件所隐含的一般假设下，研究了高斯阵列的最佳集中率。