We study the monochromatic ensemble of random functions in the generality of a compact Riemannian manifold of any dimension. We prove equidistribution of local integrals at scales within a logarithmic factor of the optimal wave scale. On the two-dimensional sphere, we prove a limit theorem for the distribution of these integrals. We also study nodal domains, giving explicit (but embarrassing) lower bounds for the Nazarov-Sodin constant in dimension 2 and 3 and an estimate of the high-dimensional behaviour.
|Commitee:||Katz, Nicholas M., Yang, Paul C.|
|School Location:||United States -- New Jersey|
|Source:||DAI-B 80/03(E), Dissertation Abstracts International|
|Keywords:||Nazarov-Sodin constant, Riemannian manifold, nodal domains|
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