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Cited by 89Analytic Number Theory ResearchSpectral Theory in Mathematical PhysicsQuantum chaos and dynamical systems

Nodal length fluctuations for arithmetic random waves

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Krishnapur, Manjunath, Kurlberg, Pär, Wigman, Igor·2013·Annals of Mathematics
DOI 10.4007/annals.2013.177.2.8
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Abstract

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.

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Authors
Krishnapur, M., Kurlberg, P., & Wigman, I.
Affiliations
  • Indian Institute of Science Bangalore (IN)
  • KTH Royal Institute of Technology (SE)
  • Cardiff University (GB)
ORCID
Venue
Annals of Mathematics
Publisher
Annals of Mathematics
Published
2013-03-01
Volume
177
Issue
2
Pages
699-737
ISSN
0003-486X (ISSN-L)
DOI
10.4007/annals.2013.177.2.8
OpenAlex
W2152885400
Cited by
89
References
0
Citations by year
2025: 2 · 2024: 8 · 2023: 8 · 2022: 8 · 2021: 7 · 2020: 15 · 2019: 10 · 2018: 11 · 2017: 5 · 2016: 8 · 2015: 4 · 2014: 2
FWCI
8.24
Type
journal article
Language
en
Open access
Locations
  • Annals of Mathematics (publishedVersion)
  • NOT FOUND REPOSITORY (Indian Institute of Science Bangalore) (acceptedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • Research Portal (King's College London) (submittedVersion)
  • arXiv (Cornell University)
Funders
Engineering and Physical Sciences Research Council (EP/J004529/1)
Topics
  • Physical Sciences › Mathematics › Algebra and Number Theory › Analytic Number Theory Research
  • Physical Sciences › Mathematics › Mathematical Physics › Spectral Theory in Mathematical Physics
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Quantum chaos and dynamical systems
Keywords
nodal length, Laplacian eigenfunctions, torus, spectral multiplicity, circle problem, irregular waves

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