On the convergence of the spectral empirical process of Wigner matrices

By Z. Bai, Jianfeng Yao. 2005

123 citations recorded by the source corpus.

Subfields: Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/0414e7b04fc70ec193c9c86330a37a38f4b22f73

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Citations in the corpus

Fluctuations of eigenvalues and second order Poincaré inequalities (2007, methodology): “An alternative approach, based on Stieltjes transforms, has been developed in Bai and Yao [5] and Bai and Silverstein [6].”
Central Limit Theorems for Linear Statistics of Heavy Tailed Random Matrices (2013, background): “…interact via a potential in [32], the set of test functions was extended and the assumptions on the entries of the Wigner matrices weakened in [7, 6, 36, 42], a more general model of band matrices was considered in [2] (see also [36, 5] for general covariance matrices), unitary matrices where…”
Sparse regular random graphs: Spectral density and eigenvectors (2009, background): “[6] Bai, Z.D. and Yao, J. (2005) On the convergence of the spectral empirical process of Wigner matrices.”
Random matrix theory in statistics: A review (2014, background): “Bai and Yao (2011) extended the scope of the results further by considering a “generalized spiked model”, where the “noise” eigenvalues of the population covariance matrix decay slowly rather than remaining constant (Fig.”
Testing in high-dimensional spiked models (2015, methodology): “The corresponding CLTs are established in Bai and Yao (2005), Bai and Silverstein (2004), and Zheng (2012) for the cases of the semi-circle, Marchenko- Pastur, and Wachter limiting distributions, respectively.”
On the sphericity test with large-dimensional observations (2013, methodology): “Throughout the paper we will use an indicator κ set to 2 when {xij} are real and to 1 when they are complex as defined in [3].”
A CLT for a band matrix model (2004, methodology): “t sketchy proofs. Earlier statements can be found in [Gi90]. A complete treatment for fanalytic in a domain including the support of the limit of the empirical distribution of eigenvalues is given in [BY03] for matrices of Wigner type, and in [BS04] for matrices ofWishart type under a certain restri”