Nodal length fluctuations for arithmetic random waves


Autoria(s): Krishnapur, Manjunath; Kurlberg, Par; Wigman, Igor
Data(s)

2013

Resumo

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.

Formato

application/pdf

Identificador

http://eprints.iisc.ernet.in/45986/1/ann_mat_177-2_699_2013.pdf

Krishnapur, Manjunath and Kurlberg, Par and Wigman, Igor (2013) Nodal length fluctuations for arithmetic random waves. In: ANNALS OF MATHEMATICS, 177 (2). pp. 699-737.

Publicador

ANNAL MATHEMATICS

Relação

http://www.math.kth.se/~kurlberg/eprints/torus-nodal.pdf

http://eprints.iisc.ernet.in/45986/

Palavras-Chave #Mathematics
Tipo

Journal Article

PeerReviewed