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dc.contributor.authorBeliaev, D
dc.contributor.authorMuirhead, S
dc.contributor.authorWigman, I
dc.date.accessioned2020-12-16T18:20:22Z
dc.date.available2020-12-16T18:20:22Z
dc.date.issued2021-02
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. https://doi.org/10.1016/j.aim.2020.107521.
dc.identifier.issn0001-8708
dc.identifier.urihttp://hdl.handle.net/11343/254344
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.languageen
dc.publisherElsevier BV
dc.titleMean conservation of nodal volume and connectivity measures for Gaussian ensembles
dc.typeJournal Article
dc.identifier.doi10.1016/j.aim.2020.107521
melbourne.affiliation.departmentSchool of Mathematics and Statistics
melbourne.source.titleAdvances in Mathematics
melbourne.source.volume378
melbourne.source.pages107521-107521
melbourne.identifier.arcDE200101467
melbourne.elementsid1483582
melbourne.internal.embargodate2023-02-12
melbourne.contributor.authorMuirhead, Stephen
dc.identifier.eissn1090-2082
melbourne.identifier.fundernameidAustralian Research Council, DE200101467
melbourne.accessrightsThis item is embargoed and will be available on 2023-02-12


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