We consider Berry's random planar wave model (1977) for a positive Laplace eigenvalue E>
0 E> 0, both in the real and complex case, and prove limit theorems for the nodal statistics …

It is shown that the topologies and nestings of the zero and nodal sets of random (Gaussian)
band‐limited functions have universal laws of distribution. Qualitative features of the …

We study local asymptotics for the spectral projector associated to a Schrödinger operator „2
CV on Rn in the semiclassical limit as „! 0. We prove local uniform convergence of the …

We consider the nodal length L (λ) of the restriction to a ball of radius r λ of a Gaussian
pullback monochromatic random wave of parameter λ> 0 associated with a Riemann …

We obtain new quantitative estimates on Weyl Law remainders under dynamical
assumptions on the geodesic flow. On a smooth compact Riemannian manifold (M, g) of …

This paper is dedicated to the study of the topologies and nesting configurations of the
components of the zero set of monochromatic random waves. We prove that the probability …

This paper concerns the asymptotic behavior of zeros and critical points for monochromatic
random waves ϕ _ λ ϕ λ of frequency λ λ on a compact, smooth, Riemannian manifold (M, g) …

Random plane wave is conjectured to be a universal model for high-energy eigenfunctions
of the Laplace operator on generic compact Riemannian manifolds. This is known to be true …

In this paper, we study the two-point Weyl Law for the Laplace-Beltrami operator on a
smooth, compact Riemannian manifold $ M $ with no conjugate points. That is, we find the …

Almost-sure asymptotics for Riemannian random waves Page 1 Bernoulli 29(1), 2023, 625–651
https://doi.org/10.3150/22-BEJ1471 Almost-sure asymptotics for Riemannian random waves …