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This paper studies the $\tau$-coherence of a (n x p)-observation matrix in aGaussian framework. The $\tau$-coherence is defined as the largest magnitudeoutside a diagonal bandwith of size $\tau$ of the empirical correlationcoefficients associated to our observations. Using the Chen-Stein method wederive the limiting law of the normalized coherence and show the convergencetowards a Gumbel distribution. We generalize here the results of Cai and Jiang[CJ11a]. We assume that the covariance matrix of the model is bandwise.Moreover, we provide numerical considerations highlighting issues from the highdimension hypotheses. We numerically illustrate the asymptotic behaviour of thecoherence with Monte-Carlo experiment using a HPC splitting strategy for highdimensional correlation matrices.

Coherence of high-dimensional random matrices in a Gaussian case : application of the Chen-Stein method