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Nodal length fluctuations for arithmetic random waves

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.

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Official URL: http://www.math.kth.se/~kurlberg/eprints/torus-nod...

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.

Item Type: Journal Article
Additional Information: Copyright for this article belongs to ANNAL MATHEMATICS, WASHINGTON RD
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Francis Jayakanth
Date Deposited: 14 Mar 2013 09:46
Last Modified: 14 Mar 2013 09:46
URI: http://eprints.iisc.ac.in/id/eprint/45986

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