Eigenvalue Distribution of Large Random Matrices

By Leonid A. Pastur, Mariya Shcherbina. 2011

458 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/cfae7c5c34a241d2a1cd74db8b6f7710e643f890

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In Statistics and Probability

Citations in the corpus

Universality for Random Tensors (2011, background): “In more familiar terms, the eigenvalue density obeys the Wigner semi-circle law under quite general assumptions [3,27,29].”
On the limiting spectral distribution for a large class of symmetric random matrices with correlated entries (2015, background): “1 in [15]) since in our case, we cannot use directly the conclusion of their theorem: we are not exactly in the situation described there.”
A Dynamical Approach to Random Matrix Theory (2017, background): “The books by Anderson, Guionnet and Zeitouni [8] and Pastur and Shcherbina [112] contain extensive material starting from the basics.”
The Elliptic Law (2012, methodology): “We will make use of the multivariate Gaussian decoupling formula [37].”
Random matrix theory in statistics: A review (2014, background): “For more detailed accounts of these topics, the reader may refer to Anderson et al. (2009), Bai and Silverstein (2009) and Pastur and Shcherbina (2011).”
Singularities of Solutions to Quadratic Vector Equations on the Complex Upper Half‐Plane (2015, background): “1) has been initiated so far that goes beyond establishing existence, uniqueness, and regularity in the regime where the parameter ́ is away from the real axis [1,23,26,35].”
Regularity conditions in the CLT for linear eigenvalue statistics of Wigner matrices (2012, methodology): “For the first integral, notice that since ν < 2/3, we are far clear from the transition region of the rescaled Hermite functions ψn, and so we can apply the asymptotics in [18] (see also [28] (5.”