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arXiv · 1707.00766

Variation of the Nazarov-Sodin constant for random plane waves and arithmetic random waves

Par Kurlberg·Igor Wigman
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Abstract

This is a manuscript containing the full proofs of results announced in [KW], together with some recent updates. We prove that the Nazarov-Sodin 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.

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Par Kurlberg, Igor Wigman. 2018-03-23. Variation of the Nazarov-Sodin constant for random plane waves and arithmetic random waves. https://arxiv.org/abs/1707.00766

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