Fine-scale properties of random functions

Publication:
Fine-scale properties of random functions

datacite.rights	open.access
dc.contributor.advisor	Sarnak, Peter
dc.contributor.author	de Courcy-Ireland, Matthew
dc.contributor.other	Mathematics Department
dc.date.accessioned	2018-10-09T21:07:52Z
dc.date.accessioned	2026-09-30T11:31:14Z
dc.date.available	2018-10-09T21:07:52Z
dc.date.available	2026-09-30T11:31:14Z
dc.date.issued	2018
dc.description.abstract	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.
dc.identifier.uri	http://arks.princeton.edu/ark:/88435/dsp01x920g0628
dc.identifier.uri	https://theses-dissertations.princeton.edu/handle/88435/dsp01x920g0628
dc.language.iso	en
dc.publisher	Princeton, NJ : Princeton University
dc.relation.isformatof	The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog: <a href=http://catalog.princeton.edu> catalog.princeton.edu </a>
dc.subject.classification	Mathematics
dc.title	Fine-scale properties of random functions
dc.type	Academic dissertations (Ph.D.)
dspace.entity.type	Publication
pu.projectgrantnumber	690-2143

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