Nodal length fluctuations for arithmetic random waves
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Thu, 20/10/2011 16:00 |
Igor Wigman (Cardiff University) |
Number Theory Seminar  |
L3 |
| Using the spectral multiplicities of the standard torus, weendow the Laplace eigenspaces with Gaussian probability measures.This induces a notion of random Gaussian eigenfunctionson the torus ("arithmetic random waves”.) We study thedistribution of the nodal length of random Laplace eigenfunctions for higheigenvalues,and our primary result is that the asymptotics for the variance isnon-universal, and is intimately related to the arithmetic oflattice points lying on a circle with radius corresponding to the energy. This work is joint with Manjunath Krishnapur and Par Kurlberg | |||