Central limit theorem for linear eigenvalue statistics of elliptic\n random matrices

2014/10/16 by Sean O’Rourke, O'Rourke, Sean, David Renfrew +1 · 1 citation
Decision Sciences · Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Probability and Risk Models #Random Matrices and Applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1410.4586

openalex publication_date 2014/10/16 · openalex created_date 2022/09/29 · openalex updated_date 2026/07/28

Abstract

We consider a class of elliptic random matrices which generalize two\nclassical ensembles from random matrix theory: Wigner matrices and random\nmatrices with iid entries. In particular, we establish a central limit theorem\nfor linear eigenvalue statistics of real elliptic random matrices under the\nassumption that the test functions are analytic. As a corollary, we extend the\nresults of Rider and Silverstein to real iid random matrices.\n

Citations

• Central Limit Theorem for linear eigenvalue statistics of the Wigner and sample covariance random matrices
• Regularity conditions in the CLT for linear eigenvalue statistics of Wigner matrices

Cited by

• CLT for LES of real valued random centrosymmetric matrices

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