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
    18 Citations
    Non-Hermitian random matrices with a variance profile (II): properties and examples.
    • 1
    • PDF
    CLT for non-Hermitian random band matrices with variance profiles
    • 3
    • PDF

    References

    SHOWING 1-10 OF 62 REFERENCES
    RANDOM MATRICES: THE CIRCULAR LAW
    • 210
    • Highly Influential
    • PDF
    Spectrum of Non-Hermitian Heavy Tailed Random Matrices
    • 46
    • PDF
    Random matrices: Universality of ESDs and the circular law
    • 324
    • Highly Influential
    • PDF
    The circular law
    • 182
    • Highly Influential
    • PDF
    Deterministic equivalents for certain functionals of large random matrices
    • 252
    • PDF
    Universality and the circular law for sparse random matrices.
    • 46
    • PDF
    Local Semicircle Law and Complete Delocalization for Wigner Random Matrices
    • 213
    • PDF
    Around the circular law
    • 141
    • Highly Influential
    • PDF