Geodesic
Nodal length fluctuations for arithmetic random waves
Manjunath Krishnapur1 ; Pär Kurlberg2 ; Igor Wigman3
1 Indian Institute of Science, Bangalore, India
2 Royal Institute of Technology, Stockholm, Sweden
3 Cardiff University, Wales, UK
Annals of mathematics, Tome 177 (2013) no. 2, pp. 699-737.

Voir la notice de l'article provenant de la source Annals of Mathematics website

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.
DOI : 10.4007/annals.2013.177.2.8

Manjunath Krishnapur 1 ; Pär Kurlberg 2 ; Igor Wigman 3

1 Indian Institute of Science, Bangalore, India
2 Royal Institute of Technology, Stockholm, Sweden
3 Cardiff University, Wales, UK 
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Manjunath Krishnapur; Pär Kurlberg; Igor Wigman. Nodal length fluctuations for arithmetic random waves. Annals of mathematics, Tome 177 (2013) no. 2, pp. 699-737. doi : 10.4007/annals.2013.177.2.8. http://geodesic.mathdoc.fr/articles/10.4007/annals.2013.177.2.8/

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