Quantitative limit theorems for local functionals of arithmetic random waves

DOI10.1007/978-3-030-01593-0_23zbMath1408.60022arXiv1702.03765OpenAlexW2595963883MaRDI QIDQ1733967

Maurizia Rossi, Giovanni Peccati

Publication date: 22 March 2019

Full work available at URL: https://arxiv.org/abs/1702.03765

zbMATH Keywords

Berry-Esseen boundsGaussian Laplace eigenfunctionsLeray measures

Mathematics Subject Classification ID

Random fields (60G60) Geometric probability and stochastic geometry (60D05) Central limit and other weak theorems (60F05) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Spectral theory; eigenvalue problems on manifolds (58C40)

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Random Lipschitz–Killing curvatures: Reduction Principles, Integration by Parts and Wiener chaos ⋮ Points on nodal lines with given direction ⋮ The asymptotic equivalence of the sample trispectrum and the nodal length for random spherical harmonics ⋮ Fluctuations of nodal sets on the 3-torus and general cancellation phenomena ⋮ Lipschitz-Killing curvatures for arithmetic random waves ⋮ Nodal statistics of planar random waves ⋮ Matrix Hermite polynomials, random determinants and the geometry of Gaussian fields ⋮ Small scale CLTs for the nodal length of monochromatic waves ⋮ A quantitative central limit theorem for the excursion area of random spherical harmonics over subdomains of S2 ⋮ Random nodal lengths and Wiener chaos ⋮ Malliavin-Stein method: a survey of some recent developments ⋮ A reduction principle for the critical values of random spherical harmonics ⋮ Gaussian random measures generated by Berry's nodal sets ⋮ Moderate Deviation estimates for Nodal Lengths of Random Spherical Harmonics ⋮ Nodal area distribution for arithmetic random waves ⋮ Phase singularities in complex arithmetic random waves

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