Volume distribution of nodal domains of random band-limited functions
Probability
2016-07-19 v2 Mathematical Physics
Differential Geometry
math.MP
Spectral Theory
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.
Keywords
Cite
@article{arxiv.1606.05766,
title = {Volume distribution of nodal domains of random band-limited functions},
author = {Dmitry Beliaev and Igor Wigman},
journal= {arXiv preprint arXiv:1606.05766},
year = {2016}
}
Comments
32 pages