Volume distribution of nodal domains of random band-limited functions

Dmitry Beliaev, Igor Wigman

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


We study the volume distribution of nodal domains of families of naturally arising Gaussian random fields on generic manifolds, namely random band-limited functions. It is found 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.

Original languageEnglish
Pages (from-to)453-492
Number of pages40
JournalProbability Theory and Related Fields
Issue number1-2
Publication statusPublished - 1 Oct 2018
Externally publishedYes


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