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Monochromatic Random Waves for General Riemannian Manifolds

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Frontiers in Analysis and Probability

Abstract

This is a survey article on some of the recent developments on monochromatic random waves defined for general Riemannian manifolds. We discuss the conditions needed for the waves to have a universal scaling limit, we review statistics for the size of their zero set and the number of their critical points, and we discuss the structure of their zero set as described by the diffeomorphism types and the nesting configurations of its components.

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Acknowledgements

The author is very grateful to her collaborators B. Hanin and P. Sarnak. The author would also like to thank the Alfred P. Sloan Foundation for their support.

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Authors and Affiliations

  1. Department of Mathematics, University of North Carolina, Chapel Hill, Chapel Hill, NC, USA

    Yaiza Canzani

Authors
  1. Yaiza Canzani
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Correspondence to Yaiza Canzani .

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Editors and Affiliations

  1. IRMA, University of Strasbourg, Strasbourg, France

    Nalini Anantharaman

  2. Institute of Mathematics, University of Zürich, Zurich, Switzerland

    Ashkan Nikeghbali

  3. Institute of Mathematics, University of Zürich, Zurich, Switzerland

    Michael Th. Rassias

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Canzani, Y. (2020). Monochromatic Random Waves for General Riemannian Manifolds. In: Anantharaman, N., Nikeghbali, A., Rassias, M.T. (eds) Frontiers in Analysis and Probability. Springer, Cham. https://doi.org/10.1007/978-3-030-56409-4_1

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