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Volume distribution of nodal domains of random band-limited functions

Research output: Contribution to journalArticlepeer-review

Dmitry Beliaev, Igor Wigman

Original languageEnglish
Number of pages453
JournalPROBABILITY THEORY AND RELATED FIELDS
Volume172
Issue number1-2
DOIs
Accepted/In press20 Oct 2017
Published3 Nov 2017

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Abstract

We study the volume distribution of nodal domains of random band-limited functions on generic manifolds, and find that in the high energy limit a typical instance obeys a deterministic universal law, independent of the manifold. Some of the basic qualitative properties of this law, such as its support, monotonicity and continuity of the cumulative probability function, are established.

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