Louis Gass

activity

20202026

most citedThe number of critical points of a Gaussian field: finiteness of moments

3 citations · 5 across the 9 of their papers we have counts for

collaborators

9 papers

math.PR2026

Scars in random waves and the FGF 1/2 universality class

Louis Gass, Giovanni Peccati, Michele Stecconi

We study the large-domain asymptotics of geometric observables in Berry's random wave model on $R^{d}$ . We show that, in sharp contrast with the behavior of stationary rando…

math.PR2025

Tightness of Stationary Nodal Measures

Louis Gass, Giovanni Peccati

We study the rescaled nodal volume field $ξ_{R}$ associated with a smooth, stationary Gaussian field on $[0, R]^{d}$ , whose covariance satisfies adequate integrability conditions. Our m…

math.PR2025

Universal Cancellations in Uniform Random Waves

Louis Gass, Domenico Marinucci, Giovanni Peccati +2

A vast literature over the past fifteen years has been devoted to the study of the geometric properties of Gaussian random waves. In this work, we investigate the geometric behavio…

math.PR2025

Zeros and critical points of Gaussian fields: cumulants asymptotics and limit theorems

Michele Ancona, Louis Gass, Thomas Letendre +1

Let $f : R^{d} \to R^{k}$ be a smooth centered stationary Gaussian field and $B \subset R^{d}$ be a bounded Borel set. In this paper, we determine the…

math.PR2025

Spectral Criteria for the Asymptotics of Local Functionals of Gaussian Fields and Their Application to Nodal Volumes and Critical Points

Louis Gass

We establish a general criterion for the positivity of the variance of a chaotic component of local functionals of stationary vector-valued Gaussian fields. This criterion is formu…

math.PR2023★ 3 cited

The number of critical points of a Gaussian field: finiteness of moments

Louis Gass, Michele Stecconi

Let $f$ be a Gaussian random field on $R^{d}$ and let $X$ be the number of critical points of $f$ contained in a compact subset. A long-standing conjecture is that, under mi…

math.PR2021★ 1 cited

Cumulants asymptotics for the zeros counting measure of real Gaussian processes

Louis Gass

We compute the exact asymptotics for the cumulants of linear statistics associated with the zeros counting measure of a large class of real Gaussian processes. Precisely, we show t…

math.PR2021

Variance of the number of zeros of dependent Gaussian trigonometric polynomials

Louis Gass

We compute the variance asymptotics for the number of real zeros of trigonometric polynomials with random dependent Gaussian coefficients and show that under mild conditions, the a…

math.PR2020★ 1 cited

Almost sure asymptotics for Riemannian random waves

Louis Gass

We consider the Riemannian random wave model of Gaussian linear combinations of Laplace eigenfunctions on a general compact Riemannian manifold. With probability one with respect t…