Expected nodal volume for non-Gaussian random band-limited functions
Abstract
The asymptotic law for the expected nodal volume of random non-Gaussian monochromatic band-limited functions is determined in vast generality. Our methods combine microlocal analytic techniques and modern probability theory. A particularly challenging obstacle needed to overcome is the possible concentration of nodal volume on a small proportion of the manifold, requiring solutions in both disciplines. As for the fine aspects of the distribution of nodal volume, such as its variance, it is expected that the non-Gaussian monochromatic functions behave qualitatively differently compared to their Gaussian counterpart, with some conjectures been put forward.
Keywords
Cite
@article{arxiv.2102.11689,
title = {Expected nodal volume for non-Gaussian random band-limited functions},
author = {Zakhar Kabluchko and Andrea Sartori and Igor Wigman},
journal= {arXiv preprint arXiv:2102.11689},
year = {2021}
}
Comments
28 pages. The statement of Corollary 5.8 was corrected, along with other more minor corrections