Mean conservation of nodal volume and connectivity measures for Gaussian ensembles

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    Author
    Beliaev, D; Muirhead, S; Wigman, I
    Date
    2021-02
    Source Title
    Advances in Mathematics
    Publisher
    Elsevier BV
    University of Melbourne Author/s
    Muirhead, Stephen
    Affiliation
    School of Mathematics and Statistics
    Metadata
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    Document Type
    Journal Article
    Citations
    Beliaev, D., Muirhead, S. & Wigman, I. (2021). Mean conservation of nodal volume and connectivity measures for Gaussian ensembles. Advances in Mathematics, 378, pp.107521-107521. https://doi.org/10.1016/j.aim.2020.107521.
    Access Status
    This item is embargoed and will be available on 2023-02-12
    URI
    http://hdl.handle.net/11343/254344
    DOI
    10.1016/j.aim.2020.107521
    Abstract
    We study in depth the nesting graph and volume distribution of the nodal domains of a Gaussian field, which have been shown in previous works to exhibit asymptotic laws. A striking link is established between the asymptotic mean connectivity of a nodal domain (i.e. the vertex degree in its nesting graph) and the positivity of the percolation probability of the field, along with a direct dependence of the average nodal volume on the percolation probability. Our results support the prevailing ansatz that the mean connectivity and volume of a nodal domain is conserved for generic random fields in dimension d = 2 but not in d _ 3, and are applied to a number of concrete motivating examples.

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