Central Limit Theorem for linear eigenvalue statistics of the Wigner and sample covariance random matrices

By Mariya Shcherbina. 2011

174 citations recorded by the source corpus.

We consider two classical ensembles of the random matrix theory: the Wigner matrices and sample covariance matrices, and prove Central Limit Theorem for linear eigenvalue statistics under rather weak (comparing with results known before) conditions on the number of derivatives of the test functions and also on the number of the entries moments. Moreover, we develop a universal method which allows one to obtain automatically the bounds for the variance of differentiable test functions, if there is a bound for the variance of the trace of the resolvent of random matrix. The method is applicable not only to the Wigner and sample covariance matrices, but to any ensemble of random matrices.

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

View Paper: https://www.semanticscholar.org/paper/631cbc79866e324209c373aeba21c4447ea81d58

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Discrete Mathematics and Combinatorics

In Mathematical Physics

In Statistics and Probability

Citations in the corpus

On finite rank deformations of Wigner matrices (2011, background): “27) The variance V(trN RN(z)) has been estimated in Proposition 2 of [30] as”
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).”
Central Limit Theorems for Linear Statistics of Heavy Tailed Random Matrices (2013, background): “…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 considered in [31, 23, 45, 22], and Chatterjee developed a general approach to these questions in…”
Regularity conditions in the CLT for linear eigenvalue statistics of Wigner matrices (2012, background): “In her proof of the CLT for linear statistics for H3/2+ functions [29], M.”