Expected nodal volume for non-Gaussian random band-limited functions

TL;DR

This paper establishes the asymptotic behavior of the expected nodal volume for non-Gaussian band-limited functions using advanced microlocal and probabilistic methods, highlighting differences from Gaussian cases.

Contribution

It provides a general asymptotic law for the expected nodal volume of non-Gaussian functions, combining microlocal analysis and probability theory to address concentration issues.

Findings

Asymptotic law for expected nodal volume established

Methods combine microlocal analysis and probability theory

Highlights differences in variance behavior from Gaussian 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.