  This paper studies the $\tau$-coherence of a (n x p)-observation matrix in a
Gaussian framework. The $\tau$-coherence is defined as the largest magnitude
outside a diagonal bandwith of size $\tau$ of the empirical correlation
coefficients associated to our observations. Using the Chen-Stein method we
derive the limiting law of the normalized coherence and show the convergence
towards 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 high
dimension hypotheses. We numerically illustrate the asymptotic behaviour of the
coherence with Monte-Carlo experiment using a HPC splitting strategy for high
dimensional correlation matrices.
