Universality of local eigenvalue statistics for some sample covariance matrices

By Gérard Ben Arous, S. P'ech'e. 2005

97 citations recorded by the source corpus.

Subfields: Discrete Mathematics and Combinatorics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/531939c4e3a8accaf77b01a6c65943bcd607aacc

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In Discrete Mathematics and Combinatorics

In Mathematical Physics

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Citations in the corpus

A necessary and sufficient condition for edge universality of Wigner matrices (2012, background): “[38] Péché, S., Soshnikov, A.: On the Lower bound of the Spectral Norm of Symmetric Random Matrices with Independent Entries, Elect.”
Universality of covariance matrices (2011, background): “In [4] Arous and Péché showed this bulk universality when dN = 1+O(N −5/48).”
Universality of local spectral statistics of random matrices (2011, methodology): “In particular, the WignerDyson-Gaudin-Mehta (WDGM) conjecture for Hermitian matrices was first solved in [27] in a joint work with the current authors and Péché, Ramı́rez, and Schlein.”
High Dimensional Statistical Inference and Random Matrices (2006, methodology): “Bulk Graphical methods [92, 93] [finance [15, 77], communications [91]] Linear Statistics Hypothesis tests, distribution theory Extremes Hypothesis tests, distribution theory, role in proofs [21, 33] Spacings [[10], otherwise few so far] General Computational tools [65], role in proofs”
Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices (2004, background): “The following result of P6ch6 [31] generalizes (8) and shows that when all but finitely many eigenvalues ek of E are 1 and those distinguished eigenvalues are "not too big," ;,1 is still not separated from the rest of the eigenvalues.”
Random Matrices: the Distribution of the Smallest Singular Values (2009, background): “Ben Arous and Peche [8] generalized Forrester’s result to matrices whose entries are gaussian summable.”
Universality of random matrices and local relaxation flow (2009, background): “The approaches of [11] and [21] are based on the following two common ingredients: (1) Johansson’s [15] result (see also [2]) stating that bulk universality holds for ensembles of the form Ĥ + sV, (1.”
Bulk universality for generalized Wigner matrices (2010, methodology): “Once such a strong form of the local semicircle law was obtained, the result of [23, 2] can be extended to a Gaussian convolution with variance only s(2) ≍ N.”
ASYMPTOTICS OF SAMPLE EIGENSTRUCTURE FOR A LARGE DIMENSIONAL SPIKED COVARIANCE MODEL (2007, background): “However, a systematic study of the individual eigenvalues has been conducted only recently by Péché (2003) and Baik, Ben Arous and Péché (2005).”
The local relaxation flow approach to universality of the local statistics for random matrices (2009, methodology): “Unfortunately, the similar formula for symmetric or quaternion self-dual Wigner matrices, as well as for real sample covariance matrices, is not very explicit and the technique of [3,14,26] cannot be extended to prove universality.”
Random matrix theory in statistics: A review (2014, methodology): “First results of this kind were proved by Johansson (2001) and were subsequently improved by Ben Arous and Péché (2005) and Johansson (2009) in the setting of Gauss divisible Hermitian ensembles for which the matrices are in the form of a Wigner matrix perturbed by a Gaussian Wigner matrix.”
Sparse regular random graphs: Spectral density and eigenvectors (2009, background): “For a comprehensive treatment of the subject, see the books by Bai and Silverstein [5] and by Anderson, Guionnet, and Zeitouni [2]; - fluctuations of the spectrum at the edge (the famous Tracy-Widom laws [62, 63, 64]) for general Wigner matrices, settled by Tao and Vu [61] and Erdős, Ramirez, Schle”
Bulk universality for Wigner matrices (2009, background): “This restriction was later removed by Ben Arous and Péché [1], who also extended this approach to Wishart ensembles).”
Rigidity of eigenvalues of generalized Wigner matrices (2010, methodology): “This result also implies the universality of the correlation functions for Hermitian Wigner ensembles [40] by combining it with the Gaussian divisible results of [26, 6] for the Step 2.”
A Dynamical Approach to Random Matrix Theory (2017, unknown): “It was later extended to complex sample covariance matrices on the entire bulk spectrum by Ben Arous and Péché [19].”
Universality of Wigner random matrices: a survey of recent results (2010, methodology): “The first rigorous partial result for bulk universality in the non-unitary case was given by Johansson [64], see also Ben Arous and Péché [11] for extending [64] to the full bulk spectrum and the recent improvement [65] on weakening moment conditions.”