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Mesoscopic Fluctuations for the Thinned Circular Unitary Ensemble
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).ORCID iD: 0000-0002-7598-4521
2017 (English)In: Mathematical physics, analysis and geometry, ISSN 1385-0172, E-ISSN 1572-9656, Vol. 20, no 3, 19Article in journal (Refereed) Published
Abstract [en]

In this paper we study the asymptotic behavior of mesoscopic fluctuations for the thinned Circular Unitary Ensemble. The effect of thinning is that the eigenvalues start to decorrelate. The decorrelation is stronger on the larger scales than on the smaller scales. We investigate this behavior by studying mesoscopic linear statistics. There are two regimes depending on the scale parameter and the thinning parameter. In one regime we obtain a CLT of a classical type and in the other regime we retrieve the CLT for CUE. The two regimes are separated by a critical line. On the critical line the limiting fluctuations are no longer Gaussian, but described by infinitely divisible laws. We argue that this transition phenomenon is universal by showing that the same transition and their laws appear for fluctuations of the thinned sine process in a growing box. The proofs are based on a Riemann-Hilbert problem for integrable operators.

Place, publisher, year, edition, pages
SPRINGER , 2017. Vol. 20, no 3, 19
Keyword [en]
Random matrices, Central Limit Theorems, Linear statistics, Mesoscopic scales, Riemann-Hilbert problems
National Category
Mathematics Physical Sciences
Identifiers
URN: urn:nbn:se:kth:diva-210963DOI: 10.1007/s11040-017-9250-4ISI: 000404329900001Scopus ID: 2-s2.0-85021200344OAI: oai:DiVA.org:kth-210963DiVA: diva2:1122620
Funder
Knut and Alice Wallenberg FoundationSwedish Research Council
Note

QC 20170712

Available from: 2017-07-12 Created: 2017-07-12 Last updated: 2017-07-12Bibliographically approved

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Berggren, TomasDuits, Maurice

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