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Dissertation/Thesis Abstract

Fine-scale Properties of Random Functions
by Courcy-Ireland, Matthew de, Ph.D., Princeton University, 2018, 138; 10933151
Abstract (Summary)

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.

Indexing (document details)
Advisor: Sarnak, Peter
Commitee: Katz, Nicholas M., Yang, Paul C.
School: Princeton University
Department: Mathematics
School Location: United States -- New Jersey
Source: DAI-B 80/03(E), Dissertation Abstracts International
Subjects: Mathematics
Keywords: Nazarov-Sodin constant, Riemannian manifold, nodal domains
Publication Number: 10933151
ISBN: 978-0-438-53596-1
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