  We derive the universality principle for empirical spectral distributions of
sample covariance matrices and their Stieltjes transforms. This principle
states the following. Suppose quadratic forms of random vectors $y_p$ in $R^p$
satisfy a weak law of large numbers and the sample size grows at the same rate
as $p$. Then the limiting spectral distribution of corresponding sample
covariance matrices is the same as in the case with conditionally Gaussian
$y_p$. This result is generalized for $m$-dependent martingale difference
sequences and $m$-dependent linear processes.
