This is a comprehensive review of the nodal domains and lines of quantum billiards,
emphasizing a quantitative comparison of theoretical findings to experiments. The nodal …

We study the asymptotic laws for the spatial distribution and the number of connected
components of zero sets of smooth Gaussian random functions of several real variables. The …

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 derive a covariance formula for the class of 'topological events' of smooth Gaussian
fields on manifolds; these are events that depend only on the topology of the level sets of the …

We study the volume distribution of nodal domains of families of naturally arising Gaussian
random fields on generic manifolds, namely random band-limited functions. It is found that in …

This article concerns new off-diagonal estimates on the remainder and its derivatives in the
pointwise Weyl law on a compact n-dimensional Riemannian manifold. As an application …

Depuis l'expérience de Chladni à la fin du XVIIIème siècle, les lignes nodales des fonctions
propres du laplacien fascinent: la manière dont leur forme varie en fonction de la fréquence …

We study the asymptotic properties of the conormal cycle of nodal sets associated to a
random superposition of eigenfunctions of the Laplacian on a smooth compact Riemannian …

In 2017, Benatar and Maffucci arXiv: 1708.07015 established an asymptotic law for the
variance of the nodal surface of arithmetic random waves on the 3-torus in the high-energy …

This article concerns new off-diagonal estimates on the remainder and its derivatives in the
pointwise Weyl law on a compact n-dimensional Riemannian manifold. As an application …