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

Author:

Sartori AndreaORCID,Wigman IgorORCID

Abstract

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.

Publisher

Cambridge University Press (CUP)

Subject

Computational Mathematics,Discrete Mathematics and Combinatorics,Geometry and Topology,Mathematical Physics,Statistics and Probability,Algebra and Number Theory,Theoretical Computer Science,Analysis

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