The expected nodal volume of non-Gaussian random band-limited functions, and their doubling index
نویسندگان
چکیده
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 possible concentration on a small portion manifold, requiring solutions both disciplines and, particular, study distribution doubling index functions. As fine aspects volume, such as its variance, it behave qualitatively differently compared their Gaussian counterpart. Some conjectures pertaining these are put forward within this manuscript.
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ژورنال
عنوان ژورنال: Forum of Mathematics, Sigma
سال: 2023
ISSN: ['2050-5094']
DOI: https://doi.org/10.1017/fms.2023.74