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We obtain the limiting spectral distribution for large sample covariancematrices associated with random vectors having graph-dependent entries underthe assumption that the interdependence among the entries grows with the samplesize n. Our results are tight. In particular, they give necessary andsufficient conditions for the Marchenko-Pastur theorem for sample covariancematrices with m-dependent orthonormal elements when m = o(n).

Limiting spectral distribution for large sample covariance matrices with graph-dependent elements