On the empirical spectral distribution for certain models related to sample covariance matrices with different correlations

Given [Formula: see text], we study two classes of large random matrices the form text] where for every are iid copies a variable (not necessarily independent) sets independent vectors having different covariance and generating well concentrated bilinear forms. We consider main asymptotic regimes as text]: standard one, slightly modified while some text]. Assuming that normalized isotropic “in average”, prove convergence in probability empirical spectral distributions to version Marchenko–Pastur law so-called effective medium distribution, correspondingly. In particular, choosing Rademacher variables regime one can get shifted semicircle laws. also apply our results certain block structures, which were studied [G. M. Cicuta, J. Krausser, R. Milkus A. Zaccone, Unifying model matrix theory arbitrary space dimensions, Phys. Rev. E 97(3) (2018) 032113, MR3789138; Pernici G. Proof conjecture on infinite dimension limit unifying theory, Stat. 175 (2) (2019) 384–401, MR3968860].