Variation of the NazarovSodin constant for random plane waves and arithmetic random waves
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This is joint work with Par Kurlberg.
We prove that the NazarovSodin constant, which up to a natural scaling gives the leading order growth for the expected number of nodal components of a random Gaussian field, genuinely depends on the field. We then infer the same for “arithmetic random waves”, i.e. random toral Laplace eigenfunctions.
This talk is part of the Probability series.
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