Sample covariance matrix is one of main objects in the
multivariate analysis in statistics. Contrary to the traditional
study, of current interest is the case when the number of
variables of a sample (ex. weather observation positions) is
comparable to the sample size (ex. daily observation). The
interest in this talk is the behavior of the largest eigenvalue of
sample covariance matrix when both the sample size and the number
of variables become large. We will restrict to the case when the
sample matrix is complex and Gaussian. The main interest is the
effect of the non-homogeneity of the eigenvalues of the covariance
matrix to the eigenvalues of the sample covariance matrix in the
limit. The method is an adaptation of random matrix theory and
part of the presentation is a joint work (in progress) with Gerard
Ben Arous and Sandrine Pich\'e.
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