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Variation of the Nazarov-Sodin constant for random plane waves and arithmetic random waves
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0003-4734-5092
King's College London.ORCID iD: 0000-0002-6152-4743
2018 (English)In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 330, p. 516-552Article in journal (Refereed) Published
Abstract [en]

This is a manuscript containing the full proofs of results announced in [10], 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. (C) 2018 Elsevier Inc. All rights reserved.

Place, publisher, year, edition, pages
ACADEMIC PRESS INC ELSEVIER SCIENCE , 2018. Vol. 330, p. 516-552
Keywords [en]
Nodal components, Nazarov-Sodin constant, Spectral measure, Weak-* topology, Continuity, Arithmetic random waves
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-249657DOI: 10.1016/j.aim.2018.03.026ISI: 000431472100015Scopus ID: 2-s2.0-85056237337OAI: oai:DiVA.org:kth-249657DiVA, id: diva2:1305081
Note

QC 20190415

Available from: 2019-04-15 Created: 2019-04-15 Last updated: 2019-04-15Bibliographically approved

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Kurlberg, Pär

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