• DOI:10.1214/18-EJP230
Corpus ID: 125469232

Non-Hermitian random matrices with a variance profile (I): deterministic equivalents and limiting ESDs

@article{Cook2016NonHermitianRM,
  title={Non-Hermitian random matrices with a variance profile (I): deterministic equivalents and limiting ESDs},
  author={N. Cook and W. Hachem and J. Najim and David Renfrew},
  journal={Electronic Journal of Probability},
  year={2016},
  volume={23},
  pages={1-61}
}

N. Cook, W. Hachem, +1 author David Renfrew

Published 2016

Mathematics

Electronic Journal of Probability

For each n, let An = (σij) be an n × n deterministic matrix and let Xn = (Xij) be an n × n random matrix with i.i.d. centered entries of unit variance. We study the asymptotic behavior of the empirical spectral distribution µ Y n of the rescaled entry-wise product Yn = 1 √ n σijXij. For our main result we provide a deterministic sequence of probability measures µn, each described by a family of Master Equations, such that the difference µ Y n − µn converges weakly in probability to the zero… CONTINUE READING

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