  Recently in Gao and Stoev (2018) 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 more general
assumptions than the ones implied by the classic condition of Berman (1964).
