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A note on the reduction principle for the nodal length of planar random waves

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  • Vidotto, Anna

Abstract

Inspired by Marinucci et al. (2020), we prove that the nodal length of a planar random wave BE, i.e. the length of its zero set BE−1(0), is asymptotically equivalent, in the L2-sense and in the high-frequency limit E→∞, to the integral of H4(BE(x)), H4 being the fourth Hermite polynomial. As straightforward consequences, we obtain Moderate Deviation estimates and a central limit theorem in Wasserstein distance. This complements recent findings by Nourdin et al. (2019) and Peccati and Vidotto (2020).

Suggested Citation

  • Vidotto, Anna, 2021. "A note on the reduction principle for the nodal length of planar random waves," Statistics & Probability Letters, Elsevier, vol. 174(C).
    • Handle: RePEc:eee:stapro:v:174:y:2021:i:c:s0167715221000523
    DOI: 10.1016/j.spl.2021.109090
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    References listed on IDEAS

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    1. Cammarota, Valentina & Marinucci, Domenico, 2020. "A reduction principle for the critical values of random spherical harmonics," Stochastic Processes and their Applications, Elsevier, vol. 130(4), pages 2433-2470.
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    Cited by:

    1. Todino, Anna Paola, 2024. "No smooth phase transition for the nodal length of band-limited spherical random fields," Stochastic Processes and their Applications, Elsevier, vol. 169(C).

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