Counting open nodal lines of random waves on planar domains

2008/10/07 by John A. Toth, Toth, John A., Igor Wigman +1
Mathematics · #35B05 #35Q99 #60G15 #FOS: Mathematics #FOS: Physical sciences #Geometry and complex manifolds #Mathematical Physics (math-ph) #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.0810.1276

openalex publication_date 2008/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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→∞. Our results are consistent with the predictions in the physics literature made by Blum, Gnutzmann and Smilansky \citeBGS.

Citations

• Singularities of boundary value problems. I

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