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 ' underlying correlation matrix, even when the latter is very close to the identity .