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arXiv · 0810.1276

Counting open nodal lines of random waves on planar domains

John A. Toth·Igor Wigman
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Abstract

We 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}.

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John A. Toth, Igor Wigman. 2009-03-17. Counting open nodal lines of random waves on planar domains. https://arxiv.org/abs/0810.1276

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