Stein-Malliavin Approximations for Nonlinear Functionals of Random Eigenfunctions on S^d
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In this paper, the authors investigated Stein-Malliavin approximations for nonlinear functionals of geometric interest for random eigenfunctions on the unit d-dimensional sphere S d, d ≥ 2.About:
This article is published in Journal of Functional Analysis.The article was published on 2015-04-15 and is currently open access. It has received 46 citations till now. The article focuses on the topics: Gegenbauer polynomials & Hermite polynomials.read more
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Non-Universality of Nodal Length Distribution for Arithmetic Random Waves
TL;DR: In particular, Krishnapur et al. as discussed by the authors showed that arithmetic random wave nodal length converges to a non-universal (non-Gaussian) limiting distribution, depending on the angular distribution of lattice points lying on circles.
Journal ArticleDOI
A quantitative central limit theorem for the Euler–Poincaré characteristic of random spherical eigenfunctions
TL;DR: In this paper, the central limit theorem for the Euler-Poincare characteristic of excursion sets of random spherical eigenfunctions in dimension 2 was established based on a decomposition of Euler's characteristic into different Wiener-chaos components: its asymptotic behaviour is dominated by a single term corresponding to the chaotic component of order two.
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Fluctuations of the nodal length of random spherical harmonics
Igor Wigman,Igor Wigman +1 more
TL;DR: In this article, the authors studied the length distribution of the nodal lines of random spherical harmonics and showed that the expected length is of order $n, while the variance should be of order Ω(n) due to the natural scaling.
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Non-Universality of Nodal Length Distribution for Arithmetic Random Waves
TL;DR: In this paper, it was shown that arithmetic random wave nodal length converges to a non-universal (non-Gaussian) limiting distribution, depending on the angular distribution of lattice points lying on circles.
References
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Orthogonal Polynomials
TL;DR: In this paper, different aspects of the theory of orthogonal polynomials of one (real or complex) variable are reviewed and orthogonality on the unit circle is not discussed.
Book
Introduction to Fourier Analysis on Euclidean Spaces.
Elias M. Stein,Guido Weiss +1 more
TL;DR: In this paper, the authors present a unified treatment of basic topics that arise in Fourier analysis, and illustrate the role played by the structure of Euclidean spaces, particularly the action of translations, dilatations, and rotations.
Book
Random Fields and Geometry
Robert J. Adler,Jonathan Taylor +1 more
TL;DR: Random Fields and Geometry as discussed by the authors is a comprehensive survey of the general theory of Gaussian random fields with a focus on geometric problems arising in the study of random fields, including continuity and boundedness, entropy and majorizing measures, Borell and Slepian inequalities.
Journal ArticleDOI
Regular and irregular semiclassical wavefunctions
TL;DR: The form of the wavefunction psi for a semiclassical regular quantum state (associated with classical motion on an N-dimensional torus in the 2N-dimensional phase space) is very different from the form of psi for an irregular state associated with stochastic classical motion in all or part of the (2N-1) energy surface in phase space as discussed by the authors.