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dc.contributor.authorBeliaev, D
dc.contributor.authorMuirhead, S
dc.contributor.authorWigman, I
dc.identifier.citationBeliaev, D., Muirhead, S. & Wigman, I. (2021). Mean conservation of nodal volume and connectivity measures for Gaussian ensembles. Advances in Mathematics, 378, pp.107521-107521.
dc.description.abstractWe 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.
dc.publisherElsevier BV
dc.titleMean conservation of nodal volume and connectivity measures for Gaussian ensembles
dc.typeJournal Article
melbourne.affiliation.departmentSchool of Mathematics and Statistics
melbourne.source.titleAdvances in Mathematics
melbourne.contributor.authorMuirhead, Stephen
melbourne.identifier.fundernameidAustralian Research Council, DE200101467
melbourne.accessrightsThis item is embargoed and will be available on 2023-02-12

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