Before revision:  We  apply our results to the case of empirical correlation matrices, that allow us to estimate reliably the width of the spectrum of the 'true ' underlying correlation matrix, even when the latter is very close to the identity matrix .
After revision:  We apply our results to the case of empirical correlation matrices, that allow us to estimate reliably the width of the spectrum of the true correlation matrix, even when the latter is very close to the identity matrix .