Mathematics Colloquium
Speaker: Igor Wigman (Cardiff)
Title: Nodal length fluctuations for arithmetic random waves
Time: Monday, January 9, 3:30 pm
Place: Amado  233, Technion
*Note unusual room, due to conference
Colloquium Homepage:
Abstract: This work is joint with Manjunath Krishnapur and Par Kurlberg.
Using the spectral multiplicities of the standard torus, we endow the
Laplace eigenspaces with Gaussian probability measures. This induces a
notion of random Gaussian eigenfunctions on the torus ("arithmetic random
waves''.)  We study the distribution of the nodal length of random Laplace
eigenfunctions for high eigenvalues, and our primary result is that the
asymptotics for the variance is non-universal, and is intimately related
to the arithmetic of lattice points lying on a circle with radius
corresponding to the energy.
Technion Math. Net (TECHMATH)
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