The expected nodal volume of non-Gaussian random band-limited functions, and their doubling index

Andrea Sartori, Igor Wigman*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

66 Downloads (Pure)

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 that we need to overcome is the possible concentration of nodal volume on a small portion of the manifold, requiring solutions in both disciplines, and, in particular, the study of the distribution of the doubling index of random band-limited functions. As for the fine aspects of the distribution of the nodal volume, such as its variance, it is expected that the non-Gaussian monochromatic functions behave qualitatively differently compared to their Gaussian counterpart. Some conjectures pertaining to these are put forward within this manuscript.
Original languageEnglish
JournalFORUM OF MATHEMATICS SIGMA
Publication statusAccepted/In press - 2 Aug 2023

Fingerprint

Dive into the research topics of 'The expected nodal volume of non-Gaussian random band-limited functions, and their doubling index'. Together they form a unique fingerprint.

Cite this