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- Title
Volume distribution of nodal domains of random band-limited functions.
- Authors
Beliaev, Dmitry; Wigman, Igor
- Abstract
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.
- Subjects
NODAL planes; DISTRIBUTION (Probability theory); RANDOM fields; MANIFOLDS (Mathematics); LIMIT theorems; PROBABILITY theory; GAUSSIAN distribution; RANDOM functions (Mathematics)
- Publication
Probability Theory & Related Fields, 2018, Vol 172, Issue 1/2, p453
- ISSN
0178-8051
- Publication type
Article
- DOI
10.1007/s00440-017-0813-x