Universality of sample covariance matrices: CLT of the smoothed   empirical spectral distribution
  A central limit theorem (CLT) for the smoothed empirical spectral distribution of sample covariance matrices is established. Moreover, the CLTs for the smoothed quantiles of Marcenko and Pastur's law have been also developed. 
Guangming Pan, Qi-Man Shao, Wang Zhou
math.ST math.PR stat.TH