31 citations · 67 across the 18 of their papers we have counts for
21 papers
Non-asymptotic Tail Bounds for the Kostlan--Shub--Smale Field: Tensor PCA and Spherical -Spin Complexity
Jean-Marc Azaïs, Federico Dalmao, Yohann De Castro
This paper builds a hierarchy of explicit, non-asymptotic tail bounds for the supremum of the Kostlan--Shub--Smale (KSS) random field on the sphere, and applies it to two problems:…
Gaussian random field's anisotropy using excursion sets
Jean-Marc Azaïs, Federico Dalmao, Yohann De Castro
This paper addresses the problem of detecting and estimating the anisotropy of a stationary real-valued random field from a single realization of one of its excursion sets. This se…
Second Maximum of a Gaussian Random Field and Exact (t-)Spacing test
Jean-Marc Azaïs, Federico Dalmao, Yohann De Castro
In this article, we introduce the novel concept of the second maximum of a Gaussian random field defined on a Riemannian manifold: Once the field reaches its global maximum at a po…
Multivariable CLT for critical points
Jean-Marc Azaïs, Federico Dalmao, Céline Delmas
We prove a multivariate central limit theorem for the numbers of critical points with all possible indexes which lie above a level of a non-necessarily isotropic Gaussian random fi…
A total variation version of Breuer--Major Central Limit Theorem under assumption
Jürgen Angst, Federico Dalmao, Guillaume Poly
In this note, we establish a qualitative total variation version of Breuer--Major Central Limit Theorem for a sequence of the type …
On the number of roots of Sturm-Liouville random sums
Federico Dalmao, José R. León
We consider the number of roots of linear combinations of a system of orthogonal eigenfunctions of a Sturm-Liouville initial value problem with i.i.d. standard Gaussian coeffic…
A note on -monochromatic random waves and cancellation
Federico Dalmao
In this note we prove that the asymptotic variance of the nodal length of complex-valued monochromatic random waves restricted to an increasing domain in is linear in the vo…
Studying the winding number for stationary Gaussian processes using real variables
Jean-Marc Azaïs, Federico Dalmao, José R. León
We consider the winding number of planar stationary Gaussian processes defined on the line. Under mild conditions, we obtain the asymptotic variance and the Central Limit Theorem f…
On 3-dimensional Berry's model
Federico Dalmao, Anne Estrade, José León
This work aims to study the dislocation or nodal lines of 3D Berry's random wave model. Their expected length is computed both in the isotropic and anisotropic cases, being them co…
On the finiteness of the moments of the measure of level sets of random fields
Diego Armentano, Jean-Marc Azaïs, Federico Dalmao +2
General conditions on smooth real valued random fields are given that ensure the finiteness of the moments of the measure of their level sets. As a by product a new generalized Kac…
Central Limit Theorem for the volume of the zero set of Kostlan-Shub-Smale random polynomial systems
Jean-Marc Azaïs, Diego Armentano, Federico Dalmao +1
We state the Central Limit Theorem, as the degree goes to infinity, for the normalized volume of the zero set of a rectangular Kostlan-Shub-Smale random polynomial system. This pap…
Central Limit Theorem for the number of real roots of Kostlan Shub Smale random polynomial systems
Diego Armentano, Jean-Marc Azaïs, Federico Dalmao +1
We obtain a Central Limit Theorem for the normalized number of real roots of a square Kostlan-Shub-Smale random polynomial system of any size as the degree goes to infinity. A stud…
On the real zeros of random trigonometric polynomials with dependent coefficients
Jürgen Angst, Federico Dalmao, Guillaume Poly
We consider random trigonometric polynomials of the form \[ f_n(t):=\sum_{1\le k \le n} a_{k} \cos(kt) + b_{k} \sin(kt), \] whose entries and …
Asymptotic normality of high level-large time crossings of a Gaussian process
Federico Dalmao, José Rafael León, Ernesto Mordecki +1
We prove the asymptotic normality of the standardized number of crossings of a centered stationary mixing Gaussian process when both the level and the time horizon go to infinity i…
Phase Singularities in Complex Arithmetic Random Waves
Federico Dalmao, Ivan Nourdin, Giovanni Peccati +1
Complex arithmetic random waves are stationary Gaussian complex-valued solutions of the Helmholtz equation on the two-dimensional flat torus. We use Wiener-Itô chaotic expansions i…
Local universality of the number of zeros of random trigonometric polynomials with continuous coefficients
Jean-Marc Azaïs, Federico Dalmao, José León +2
Let be a random trigonometric polynomial of degree with iid coefficients and let denote the (random) number of its zeros lying in the compact interval $I\subset\…
CLT for the zeros of Kostlan Shub Smale random polynomials
Federico Dalmao
In this paper we find the asymptotic main term of the variance of the number of roots of Kostlan-Shub-Smale random polynomials and prove a central limit theorem for the number of r…
Robustness of Cucker-Smale flocking model
Eduardo Canale, Federico Dalmao, Ernesto Mordecki +1
Consider a system of autonomous interacting agents moving in space, adjusting each own velocity as a weighted mean of the relative velocities of the other agents. In order to test…
CLT for the zeros of Classical Random Trigonometric Polynomials
Jean-Marc Azaïs, Federico Dalmao, José R. León
We prove a Central Limit Theorem for the number of zeros of random trigonometric polynomials of the form , being independent standard…
Rice Formula for processes with jumps and applications
Federico Dalmao, Ernesto Mordecki
We extend Rice Formula to a process which is the sum of two independent processes: a smooth process and a pure jump process with finitely many jumps. Formulas for the mean number o…
Cucker-Smale Flocking Under Hierarchical Leadership and Random Interactions
Federico Dalmao, Ernesto Mordecki
Consider a flock of birds that fly interacting between them. The interactions are modelled through a hierarchical system in which each bird, at each time step, adjusts its own velo…