Non-universality of the Nazarov-Sodin constant
Mathematical Physics
2017-07-11 v2 math.MP
Abstract
We prove that the Nazarov-Sodin constant, which up to a natural scaling gives the leading order growth for the expected number of nodal components of a random Gaussian field, genuinely depends on the field. We then infer the same for "arithmetic random waves", i.e. random toral Laplace eigenfunctions.
Keywords
Cite
@article{arxiv.1406.7449,
title = {Non-universality of the Nazarov-Sodin constant},
author = {Par Kurlberg and Igor Wigman},
journal= {arXiv preprint arXiv:1406.7449},
year = {2017}
}
Comments
7 pages. Corrected typos