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SUMMARY:Nodal length fluctuations for arithmetic random waves. - Igor Wigm
 an\, (King's College London)
DTSTART:20130521T153000Z
DTEND:20130521T163000Z
UID:TALK45369@talks.cam.ac.uk
CONTACT:12974
DESCRIPTION:Using the spectral multiplicities of the standard torus\, we e
 ndow the Laplace eigenspaces with Gaussian probability measures. This indu
 ces a notion of random Gaussian Laplace eigenfunctions on the torus ("arit
 hmetic random waves"). We study the distribution of the nodal length of ra
 ndom eigenfunctions for large eigenvalues\, and our primary result is that
  the asymptotics for the variance is non-universal\, and is intimately rel
 ated to the arithmetic of lattice points lying on a circle with radius cor
 responding to the energy.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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