Counting open nodal lines of random waves on planar domains

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dc.creatorToth, John A.
dc.creatorWigman, Igor
dc.date2008-10-07
dc.date2009-03-17
dc.date.accessioned2026-07-07T12:52:35Z
dc.date.available2026-07-07T12:52:35Z
dc.descriptionWe compute the asymptotic expectation of the number of {\em 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 $λ\to\infty$. Our results are consistent with the predictions in the physics literature made by Blum, Gnutzmann and Smilansky \cite{BGS}.
dc.description1) We simplified the proof of the converse direction in Lemma 2.1. 2) We moved the proof of Prop. 3.2 (and Lemma 3.1) to the appendix and just stated the main results in section 3.2. We also added two references [BSZ1],[BSZ2] to papers by Bleher, Shiffman and Zeldtich in section 3.2. 3) Added references to papers about nodal volume and Yau's conjecture
dc.identifierhttps://arxiv.org/abs/0810.1276
dc.identifierhttp://arxiv.org/abs/0810.1276
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/223340
dc.subjectMathematical Physics
dc.subjectProbability
dc.subject35B05, 35Q99, 60G15
dc.titleCounting open nodal lines of random waves on planar domains
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