On the nodal structures of random fields: a decade of results

Cites Work

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Non-universality of nodal length distribution for arithmetic random waves
On the distribution of the critical values of random spherical harmonics
Nodal intersections for random waves on the 3-dimensional torus
On probability measures arising from lattice points on circles
Nodal intersections for random waves against a segment on the 3-dimensional torus
Fluctuations of the nodal length of random spherical harmonics
On the nodal sets of toral eigenfunctions
Restriction of toral eigenfunctions to hypersurfaces and nodal sets
Counting nodal lines which touch the boundary of an analytic domain
Hyperbolic distribution problems and half-integral weight Maass forms
The distribution of the lattice points on circles
On the angular distribution of Gaussian integers with fixed norm
Fluctuations of the total number of critical points of random spherical harmonics
Quantitative limit theorems for local functionals of arithmetic random waves
Random complex zeroes. I: Asymptotic normality
Asymptotic of the spectral function of a positive elliptic operator without the nontrap condition
Nodal length fluctuations for arithmetic random waves
Planck-scale distribution of nodal length of arithmetic random waves
No repulsion between critical points for planar Gaussian random fields
On the variance of the nodal volume of arithmetic random waves
Mean number and correlation function of critical points of isotropic Gaussian fields and some results on GOE random matrices
The asymptotic equivalence of the sample trispectrum and the nodal length for random spherical harmonics
Boundary effect on the nodal length for arithmetic random waves, and spectral semi-correlations
Local universality for zeros and critical points of monochromatic random waves
Nodal lengths in shrinking domains for random eigenfunctions on $S^2$
On the correlation between nodal and nonzero level sets for random spherical harmonics
Nodal intersections and geometric control
A note on the reduction principle for the nodal length of planar random waves
Phase singularities in complex arithmetic random waves
Nodal intersections of random eigenfunctions against a segment on the 2-dimensional torus
Planck-scale mass equidistribution of toral Laplace eigenfunctions
Nodal statistics of planar random waves
On nonlinear functionals of random spherical eigenfunctions
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
On the area of excursion sets of spherical Gaussian eigenfunctions
Asymptotic Laws for the Spatial Distribution and the Number of Connected Components of Zero Sets of Gaussian Random Functions
Nodal intersections for random eigenfunctions on the torus
The distribution of the zeros of random trigonometric polynomials
Topologies of Nodal Sets of Random Band‐Limited Functions
The defect variance of random spherical harmonics
Counting Open Nodal Lines of Random Waves on Planar Domains
Level Sets and Extrema of Random Processes and Fields
Real and complex zeros of Riemannian random waves
On the number of nodal domains of random spherical harmonics
On the distribution of the nodal sets of random spherical harmonics
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
On the fractal structure of attainable probability measures
On Fourier coefficients and transforms of functions of two variables
Fluctuations of nodal sets on the 3-torus and general cancellation phenomena
The defect of toral Laplace eigenfunctions and arithmetic random waves
Spectral Quasi Correlations and Phase Transitions for the Nodal Length of Arithmetic Random Waves
Nodal area distribution for arithmetic random waves
Two Point Function for Critical Points of a Random Plane Wave
A Problem on Sums of Two Squares
Random Waves On $\mathbb T^3$: Nodal Area Variance and Lattice Point Correlations
On the nodal lines of random and deterministic Laplace eigenfunctions
On 3-dimensional Berry's model
Central limit theorems for level functionals of stationary Gaussian processes and fields