We consider asymptotic behavior of the correlation functions of the characteristic polynomials of the hermitian sample covariance matrices Hn=n-1Am,n* Am,n, where A m,n is a m × n complex random matrix with independent and identically distributed entries Raαj and Iaαj. We show that for the correlation function of any even order the asymptotic behavior in the bulk and at the edge of the spectrum coincides with those for the Gaussian Unitary Ensemble up to a factor, depending only on the fourth moment of the common probability law of entries Raαj and Iaαj, i.e., the higher moments do not contribute to the above limit.
|Original language||English (US)|
|Number of pages||34|
|Journal||Probability Theory and Related Fields|
|State||Published - Jun 2013|
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty