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On Nonlinear Functionals of Random Spherical Eigenfunctions

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Abstract

We prove central limit theorems and Stein-like bounds for the asymptotic behaviour of nonlinear functionals of spherical Gaussian eigenfunctions. Our investigation combines asymptotic analysis of higher order moments for Legendre polynomials and, in addition, recent results on Malliavin calculus and total variation bounds for Gaussian subordinated fields. We discuss applications to geometric functionals like the defect and invariant statistics, e.g., polyspectra of isotropic spherical random fields. Both of these have relevance for applications, especially in an astrophysical environment.

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Authors and Affiliations

  1. Department of Mathematics, University of Rome Tor Vergata, Rome, Italy

    Domenico Marinucci

  2. Department of Mathematics, King’s College London, London, UK

    Igor Wigman

Authors
  1. Domenico Marinucci
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  2. Igor Wigman
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Correspondence to Igor Wigman.

Additional information

Communicated by S. Zelditch

Research of D.M. is supported by the ERC Grant 277742 Pascal. Research of I.W. is supported by an EPSRC Grant EP/J004529/1 under the First Grant Scheme.

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Marinucci, D., Wigman, I. On Nonlinear Functionals of Random Spherical Eigenfunctions. Commun. Math. Phys. 327, 849–872 (2014). https://doi.org/10.1007/s00220-014-1939-7

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  • DOI: https://doi.org/10.1007/s00220-014-1939-7

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