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Gaussian and non-Gaussian fluctuations for mesoscopic linear statistics in determinantal processes
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0003-2943-7006
(English)Manuscript (preprint) (Other academic)
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-186533OAI: oai:DiVA.org:kth-186533DiVA: diva2:927679
Funder
Knut and Alice Wallenberg Foundation, 67394
Note

QC 20160513

Available from: 2016-05-12 Created: 2016-05-12 Last updated: 2016-05-13Bibliographically approved
In thesis
1. Fluctuations of smooth linear statistics of determinantal point processes
Open this publication in new window or tab >>Fluctuations of smooth linear statistics of determinantal point processes
2016 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

We study eigenvalues of unitary invariant random matrices and other de-terminantal point processes. Paper A investigates some generalizations ofthe Gaussian Unitary Ensemble which are motivated by the physics of freefermions. We show that these processes exhibit a transition from Poisson tosine statistics at mesoscopic scales and that, at the critical scale, fluctuationsare not Gaussian but are governed by complicated limit laws. In papers Band C, we prove limit theorems which cover the different regimes of randommatrix theory. In particular, this establishes universality of the fluctuations ofinvariant Hermitian random matrices in great generality. The techniques arebased on generalizations of the orthogonal polynomial method and the cumu-lant method developed by Soshnikov. In particular, the results rely on certaincombinatorial identities originating in the theory of random walks and on theasymptotics for Orthogonal polynomials coming from the Riemann-Hilbertsteepest descent introduced by Deift et al.

Place, publisher, year, edition, pages
KTH Royal Institute of Technology, 2016. x, 43 p.
Series
TRITA-MAT-A, 2016-1
National Category
Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:kth:diva-186536 (URN)
Public defence
2016-06-03, Sal F3,, Lindstedtsvägen 26, KTH-Campus, Stockholm, 13:15 (English)
Opponent
Supervisors
Funder
Knut and Alice Wallenberg Foundation, 67394
Note

QC 20160513

Available from: 2016-05-13 Created: 2016-05-12 Last updated: 2016-05-13Bibliographically approved

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