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Local Law of Addition of Random Matrices on Optimal Scale
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
2017 (engelsk)Inngår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 349, nr 3, s. 947-990Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

The eigenvalue distribution of the sum of two large Hermitian matrices, when one of them is conjugated by a Haar distributed unitary matrix, is asymptotically given by the free convolution of their spectral distributions. We prove that this convergence also holds locally in the bulk of the spectrum, down to the optimal scales larger than the eigenvalue spacing. The corresponding eigenvectors are fully delocalized. Similar results hold for the sum of two real symmetric matrices, when one is conjugated by Haar orthogonal matrix.

sted, utgiver, år, opplag, sider
Springer-Verlag New York, 2017. Vol. 349, nr 3, s. 947-990
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URN: urn:nbn:se:kth:diva-202111DOI: 10.1007/s00220-016-2805-6ISI: 000393696700005Scopus ID: 2-s2.0-84995751210OAI: oai:DiVA.org:kth-202111DiVA, id: diva2:1081699
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QC 20170314

Tilgjengelig fra: 2017-03-14 Laget: 2017-03-14 Sist oppdatert: 2017-11-29bibliografisk kontrollert

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