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Nodal length fluctuations for arithmetic random waves
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0003-4734-5092
2013 (English)In: Annals of Mathematics, ISSN 0003-486X, E-ISSN 1939-8980, Vol. 177, no 2, 699-737 p.Article in journal (Refereed) Published
Abstract [en]

Using the spectral multiplicities of the standard torus, we endow the Laplace eigenspaces with Gaussian probability measures. This induces a notion of random Gaussian Laplace eigenfunctions on the torus ("arithmetic random waves"). We study the distribution of the nodal length of random eigenfunctions for large eigenvalues, and our primary result is that the asymptotics for the variance is nonuniversal. Our result is intimately related to the arithmetic of lattice points lying on a circle with radius corresponding to the energy.

Place, publisher, year, edition, pages
2013. Vol. 177, no 2, 699-737 p.
National Category
URN: urn:nbn:se:kth:diva-119093DOI: 10.4007/annals.2013.177.2.8ISI: 000314351100008ScopusID: 2-s2.0-84874791522OAI: diva2:610480
Knut and Alice Wallenberg Foundation, KAW 2005.0098Swedish Research Council

QC 20130311

Available from: 2013-03-11 Created: 2013-03-07 Last updated: 2013-03-11Bibliographically approved

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Kurlberg, Pär
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