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dc.contributor.author
Erdos, Laszlo
dc.contributor.author
Krüger, Torben
dc.contributor.author
Schröder, Dominik
dc.date.accessioned
2020-08-14T14:29:20Z
dc.date.available
2020-05-14T02:41:36Z
dc.date.available
2020-05-14T09:36:05Z
dc.date.available
2020-08-14T14:29:20Z
dc.date.issued
2020-09
dc.identifier.issn
1432-0916
dc.identifier.issn
0010-3616
dc.identifier.other
10.1007/s00220-019-03657-4
en_US
dc.identifier.uri
http://hdl.handle.net/20.500.11850/414682
dc.description.abstract
For complex Wigner-type matrices, i.e. Hermitian random matrices with independent, not necessarily identically distributed entries above the diagonal, we show that at any cusp singularity of the limiting eigenvalue distribution the local eigenvalue statistics are universal and form a Pearcey process. Since the density of states typically exhibits only square root or cubic root cusp singularities, our work complements previous results on the bulk and edge universality and it thus completes the resolution of the Wigner–Dyson–Mehta universality conjecture for the last remaining universality type in the complex Hermitian class. Our analysis holds not only for exact cusps, but approximate cusps as well, where an extended Pearcey process emerges. As a main technical ingredient we prove an optimal local law at the cusp for both symmetry classes. This result is also the key input in the companion paper (Cipolloni et al. in Pure Appl Anal, 2018. arXiv:1811.04055) where the cusp universality for real symmetric Wigner-type matrices is proven. The novel cusp fluctuation mechanism is also essential for the recent results on the spectral radius of non-Hermitian random matrices (Alt et al. in Spectral radius of random matrices with independent entries, 2019. arXiv:1907.13631), and the non-Hermitian edge universality (Cipolloni et al. in Edge universality for non-Hermitian random matrices, 2019. arXiv:1908.00969).
en_US
dc.language.iso
en
en_US
dc.publisher
Springer
en_US
dc.title
Cusp Universality for Random Matrices I: Local Law and the Complex Hermitian Case
en_US
dc.type
Journal Article
dc.date.published
2020-04-28
ethz.journal.title
Communications in Mathematical Physics
ethz.journal.volume
378
en_US
ethz.journal.issue
2
en_US
ethz.journal.abbreviated
Commun. Math. Phys.
ethz.pages.start
1203
en_US
ethz.pages.end
1278
en_US
ethz.identifier.wos
ethz.identifier.scopus
ethz.publication.place
Berlin
en_US
ethz.publication.status
published
en_US
ethz.date.deposited
2020-05-14T02:41:40Z
ethz.source
WOS
ethz.eth
yes
en_US
ethz.availability
Metadata only
en_US
ethz.rosetta.installDate
2020-08-14T14:29:31Z
ethz.rosetta.lastUpdated
2020-08-14T14:29:31Z
ethz.rosetta.versionExported
true
ethz.COinS
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