Matrix Hermite polynomials, random determinants and the geometry of Gaussian fields

DOI10.5802/ahl.183arXiv2109.13749OpenAlexW3204324731MaRDI QIDQ6191444

Publication date: 7 March 2024

Published in: Annales Henri Lebesgue (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2109.13749

zbMATH Keywords

generalized Hermite polynomials Gaussian random matrices limit theorems zonal polynomials arithmetic random waves Wiener chaos expansions intrinsic and mixed volumes

Mathematics Subject Classification ID

Random fields (60G60) Geometric probability and stochastic geometry (60D05) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Convergence of probability measures (60B10)

Related Items (1)

Asymptotic distribution of nodal intersections for ARW against a surface

Cites Work

Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Non-universality of nodal length distribution for arithmetic random waves
On the distribution of the critical values of random spherical harmonics
Fluctuations of the nodal length of random spherical harmonics
Zonal polynomials of the real positive definite symmetric matrices
Expected absolute random determinants and zonoids
Asymptotic distributions of the latent roots of the covariance matrix with multiple population roots
On the total variation of the Jacobian.
On a coupling of solutions to the interface stochastic differential equation on a star graph
Quantitative limit theorems for local functionals of arithmetic random waves
Statistics on special manifolds
Bilinear forms and zonal polynomials
Nodal length fluctuations for arithmetic random waves
Random determinants, mixed volumes of ellipsoids, and zeros of Gaussian random fields
Gaussian random measures generated by Berry's nodal sets
Phase singularities in complex arithmetic random waves
Nodal statistics of planar 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
On the distribution of the latent roots of a positive definite random symmetric matrix. I
Fluctuations of the Euler-Poincaré characteristic for random spherical harmonics
Normal Approximations with Malliavin Calculus
Random Fields on the Sphere
Weak notions of Jacobian determinant and relaxation
Hermite Expansions on ℝ n for Radial Functions
Stochastic and Integral Geometry
Level Sets and Extrema of Random Processes and Fields
Regular and irregular semiclassical wavefunctions
Statistics of nodal lines and points in chaotic quantum billiards: perimeter corrections, fluctuations, curvature
Rotational symmetry of the Hermite projection operators
Fluctuations of nodal sets on the 3-torus and general cancellation phenomena
Nodal area distribution for arithmetic random waves
Random Fields and Geometry
Random Waves On $\mathbb T^3$: Nodal Area Variance and Lattice Point Correlations
Orientation statistics
On 3-dimensional Berry's model

This page was built for publication: Matrix Hermite polynomials, random determinants and the geometry of Gaussian fields