Michele Stecconi

activity

20192026

most citedGeometry and topology of spin random fields

4 citations · 11 across the 17 of their papers we have counts for

collaborators

19 papers

math.PR2026

Statistics on Yau's conjecture: Variance asymptotics

Michele Stecconi, Anna Paola Todino

We investigate the probabilistic counterpart of Yau's conjecture on the nodal volume of Laplace eigenfunctions on compact manifolds, by studying the high-frequency variance asympto…

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

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

Level area of spin random fields: a chaos decomposition

Francesca Pistolato, Michele Stecconi

We study real left-invariant spin Gaussian fields on $S O (3)$ , a special class of non-isotropic random fields used to model the polarization of the Cosmic Microwave Background. Leve…

math.PR2025

New chaos decomposition of Gaussian nodal volumes

Michele Stecconi, Anna Paola Todino

We investigate the random variable defined by the volume of the zero set of a smooth Gaussian field, on a general Riemannian manifold possibly with boundary, a fundamental object i…

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.PR2024

Critical Points of Chi-Fields

Domenico Marinucci, Michele Stecconi

We give here a semi-analytic formula for the density of critical values for chi random fields on a general manifold. The result uses Kac-Rice argument and a convenient representati…

math.PR2024

Expected Lipschitz-Killing curvatures for spin random fields and other non-isotropic fields

Francesca Pistolato, Michele Stecconi

Spherical spin random fields are used to model the Cosmic Microwave Background polarization, the study of which is at the heart of modern Cosmology and will be the subject of the L…

math.PR2024

Nodal Volumes as Differentiable Functionals of Gaussian fields

Giovanni Peccati, Michele Stecconi

We characterize the absolute continuity of the law and the Malliavin-Sobolev regularity of random nodal volumes associated with smooth Gaussian fields on generic $C^{2}$ ma…

math.AG2023

The probabilistic method in real singularity theory

Antonio Lerario, Michele Stecconi

We explain how to use the probabilistic method to prove the existence of real polynomial singularities with rich topology, i.e. with total Betti number of the maximal possible orde…

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.PR2022★ 1 cited

Expectation of a random submanifold: the zonoid section

Léo Mathis, Michele Stecconi

We develop a calculus based on zonoids - a special class of convex bodies - for the expectation of functionals related to a random submanifold $Z$ defined as the zero set of a smoo…

math.PR2022★ 4 cited

Geometry and topology of spin random fields

Antonio Lerario, Domenico Marinucci, Maurizia Rossi +1

Spin (spherical) random fields are very important in many physical applications, in particular they play a key role in Cosmology, especially in connection with the analysis of the…

math.DG2021

Random Differential Topology

Michele Stecconi

This manuscript collects three independent works: arXiv:1902.03805, arXiv:1906.04444, with Antonio Lerario and arXiv:2103.10853, together with some additional results, observations…

math.PR2021

Isotropic random spin weighted functions on $S^{2}$ vs isotropic random fields on $S^{3}$

Michele Stecconi

We show that an isotropic random field on $S U (2)$ is not necessarily isotropic as a random field on $S^{3}$ , although the two spaces can be identified. The ambiguity is due to the fa…

math.PR2021

Kac-Rice formula for transverse intersections

Michele Stecconi

We prove a generalized Kac-Rice formula that, in a well defined regular setting, computes the expected cardinality of the preimage of a submanifold via a random map, by expressing…

math.DG2020

What is the Degree of a Smooth Hypersurface?

Antonio Lerario, Michele Stecconi

Let $D$ be a disk in $R^{n}$ and $f \in C^{r + 2} (D, R^{k})$ . We deal with the problem of the algebraic approximation of the set $j^{r} f^{- 1} (W)$ consisting of the set o…

math.AG2019★ 2 cited

Maximal and Typical Topology of Real Polynomial Singularities

Antonio Lerario, Michele Stecconi

Given a polynomial map $ψ : S^{m} \to R^{k}$ with components of degree $d$ , we investigate the structure of the semialgebraic set $Z \subseteq S^{m}$ consisting of those points wher…

math.DG2019★ 1 cited

Differential Topology of Gaussian Random Fields

Antonio Lerario, Michele Stecconi

Motivated by numerous questions in random geometry, given a smooth manifold $M$ , we approach a systematic study of the differential topology of Gaussian random fields (GRF) $X:M\to…

Statistics on Yau's conjecture: Variance asymptotics

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

Universal Cancellations in Uniform Random Waves

Level area of spin random fields: a chaos decomposition

New chaos decomposition of Gaussian nodal volumes

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

Critical Points of Chi-Fields

Expected Lipschitz-Killing curvatures for spin random fields and other non-isotropic fields

Nodal Volumes as Differentiable Functionals of Gaussian fields

The probabilistic method in real singularity theory

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

Expectation of a random submanifold: the zonoid section

Geometry and topology of spin random fields

Random Differential Topology

Isotropic random spin weighted functions on S2 vs isotropic random fields on S3

Kac-Rice formula for transverse intersections

What is the Degree of a Smooth Hypersurface?

Maximal and Typical Topology of Real Polynomial Singularities

Differential Topology of Gaussian Random Fields

Isotropic random spin weighted functions on $S^{2}$ vs isotropic random fields on $S^{3}$