Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
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
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-119093DOI: 10.4007/annals.2013.177.2.8ISI: 000314351100008Scopus ID: 2-s2.0-84874791522OAI: oai:DiVA.org:kth-119093DiVA: diva2:610480
Funder
Knut and Alice Wallenberg Foundation, KAW 2005.0098Swedish Research Council
Note

QC 20130311

Available from: 2013-03-11 Created: 2013-03-07 Last updated: 2017-12-06Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full textScopus

Authority records BETA

Kurlberg, Pär

Search in DiVA

By author/editor
Kurlberg, Pär
By organisation
Mathematics (Div.)
In the same journal
Annals of Mathematics
Mathematics

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 41 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf