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Universality for certain Hermitian Wigner matrices under weak moment conditions
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0003-2943-7006
2012 (English)In: Annales de l'I.H.P. Probabilites et statistiques, ISSN 0246-0203, Vol. 48, no 1, 47-79 p.Article in journal (Refereed) Published
Abstract [en]

We study the universality of the local eigenvalue statistics of Gaussian divisible Hermitian Wigner matrices. These random matrices are obtained by adding an independent GUE matrix to an Hermitian random matrix with independent elements, a Wigner matrix. We prove that Tracy-Widom universality holds at the edge in this class of random matrices under the optimal moment condition that there is a uniform bound on the fourth moment of the matrix elements. Furthermore, we show that universality holds in the bulk for Gaussian divisible Wigner matrices if we just assume finite second moments.

Place, publisher, year, edition, pages
2012. Vol. 48, no 1, 47-79 p.
Keyword [en]
Wigner matrix, Gaussian divisible, Optimal moment condition, Universality, Tracy-Widom distribution
National Category
URN: urn:nbn:se:kth:diva-91262DOI: 10.1214/11-AIHP429ISI: 000300338800002ScopusID: 2-s2.0-84856276225OAI: diva2:509060
Swedish Research CouncilKnut and Alice Wallenberg Foundation, KAW2010.0063
QC 20120312Available from: 2012-03-12 Created: 2012-03-12 Last updated: 2012-03-12Bibliographically approved

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