Counting Open Nodal Lines of Random Waves on Planar Domains

Toth, J. A. and Wigman, Igor 2009. Counting Open Nodal Lines of Random Waves on Planar Domains. International Mathematics Research Notices 2009 (18) , pp. 3337-3365. 10.1093/imrn/rnp052

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Abstract

We compute the asymptotic expectation of the number of open nodal lines for random waves on smooth planar domains. We find that for both the long energy window [0, λ], and the short one [λ, λ +1], the expected number of open nodal lines is proportional to λ, asymptotically as λ → ∞. Our results are consistent with the predictions of Blum, Gnutzmann, and Smilansky [4] in the physics literature.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	Oxford University Press
ISSN:	1073-7928
Last Modified:	26 Jun 2019 01:57
URI:	https://orca.cardiff.ac.uk/id/eprint/12412

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