Volume distribution of nodal domains of random band-limited functions
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🧮 math.PR
math-phmath.DGmath.MPmath.SP
keywords
band-limiteddistributiondomainsfunctionsnodalrandomvolumebasic
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We study the volume distribution of nodal domains of random band-limited functions on generic manifolds, and find that in the high energy limit a typical instance obeys a deterministic universal law, independent of the manifold. Some of the basic qualitative properties of this law, such as its support, monotonicity and continuity of the cumulative probability function, are established.
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