Nodal statistics of planar random waves
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Publication:2421535
DOI10.1007/s00220-019-03432-5zbMath1431.60025arXiv1708.02281OpenAlexW2963644465MaRDI QIDQ2421535
Giovanni Peccati, Ivan Nourdin, Maurizia Rossi
Publication date: 17 June 2019
Published in: Communications in Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1708.02281
Random fields (60G60) Central limit and other weak theorems (60F05) Spectral problems; spectral geometry; scattering theory on manifolds (58J50)
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Cites Work
- Non-universality of nodal length distribution for arithmetic random waves
- On the distribution of the critical values of random spherical harmonics
- On probability measures arising from lattice points on circles
- Fluctuations of the nodal length of random spherical harmonics
- Nodal sets of eigenfunctions on Riemannian manifolds
- Eigenfunctions and nodal sets
- A quantitative central limit theorem for the Euler-Poincaré characteristic of random spherical eigenfunctions
- Quantitative limit theorems for local functionals of arithmetic random waves
- \(C^\infty\) scaling asymptotics for the spectral projector of the Laplacian
- Nodal length fluctuations for arithmetic random waves
- The asymptotic equivalence of the sample trispectrum and the nodal length for random spherical harmonics
- Local universality for zeros and critical points of monochromatic random waves
- Phase singularities in complex arithmetic random waves
- On the volume of nodal sets for eigenfunctions of the Laplacian on the torus
- The Leray measure of nodal sets for random eigenfunctions on the torus
- Central limit theorems for sequences of multiple stochastic integrals
- Fluctuations of the Euler-Poincaré characteristic for random spherical harmonics
- On the area of excursion sets of spherical Gaussian eigenfunctions
- Normal Approximations with Malliavin Calculus
- Nodal intersections for random eigenfunctions on the torus
- Random Fields on the Sphere
- Level Sets and Extrema of Random Processes and Fields
- Real and complex zeros of Riemannian random waves
- Regular and irregular semiclassical wavefunctions
- Statistics of nodal lines and points in chaotic quantum billiards: perimeter corrections, fluctuations, curvature
- Asymptotic distribution of nodal intersections for arithmetic random waves
- Universality of the nodal length of bivariate random trigonometric polynomials
- Approximations for the Bessel and Airy functions with an explicit error term
- Nodal area distribution for arithmetic random waves
- Random Fields and Geometry
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
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