Central Limit Theorem for Linear Eigenvalue Statistics for Submatrices of Wigner Random Matrices

Lingyun Li; Matthew Reed; Alexander Soshnikov

doi:10.3389/fams.2020.00017

Frontiers in Applied Mathematics and Statistics (Jun 2020)

Central Limit Theorem for Linear Eigenvalue Statistics for Submatrices of Wigner Random Matrices

Lingyun Li,
Matthew Reed,
Alexander Soshnikov

Affiliations

Lingyun Li: Department of Mathematics, Beijing Technology and Business University, Beijing, China
Matthew Reed: Department of Mathematics, University of California, Davis, Davis, CA, United States
Alexander Soshnikov: Department of Mathematics, University of California, Davis, Davis, CA, United States

DOI: https://doi.org/10.3389/fams.2020.00017
Journal volume & issue: Vol. 6

Abstract

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We prove the Central Limit Theorem for finite-dimensional vectors of linear eigenvalue statistics of submatrices of Wigner random matrices under the assumption that test functions are sufficiently smooth. We connect the asymptotic covariance to a family of correlated Gaussian Free Fields.

Published in Frontiers in Applied Mathematics and Statistics

ISSN: 2297-4687 (Online)
Publisher: Frontiers Media S.A.
Country of publisher: Switzerland
LCC subjects: Technology: Technology (General): Industrial engineering. Management engineering: Applied mathematics. Quantitative methods; Science: Mathematics: Probabilities. Mathematical statistics
Website: http://journal.frontiersin.org/journal/applied-mathematics-and-statistics#

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