content_image/310939.jpg content_image/310938.jpg content_image/310937.jpg content_image/310935.jpg content_image/310936.jpg content_image/310934.jpg
stein (2004). The same theorem implies that 

<img src='content_image/310939.jpg'>

where ¯ z$_{j}$$_{0}$ = lim z$_{j}$$_{0}$ as n, p → ∞ , 

<img src='content_image/310938.jpg'>

and 

<img src='content_image/310937.jpg'>

where 

with m ( z ) given by (3.6) of OMH, where c$_{p}$ is replaced by c. That is, 

<img src='content_image/310935.jpg'>

<img src='content_image/310936.jpg'>

where the branch of the square root is chosen so that the real and the imaginary parts of √ ( z − c − 1) 2 − 4 c have the same signs as the real and the imaginary parts of z − c − 1, respectively. The contours of integration in (54)-(56) are closed, oriented counterclockwise, enclose zero and the support of the Marchenko-Pastur distribution with parameter c , and do not enclose ¯ z$_{j}$$_{0}$ . 

The above expressions can be simplified. Use formula 1.16 of Bai and Silverstein (2004), to get 

<img src='content_image/310934.jpg'>

