Michele Stecconi
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Michele Stecconi has a total of 7 co-authors. Here are the top co-authors by number of shared publications:
- Antonio Lerario
SISSA, Trieste, Italy
2 shared publications - Domenico Marinucci
Department of Mathematics University of Rome Tor Vergata
2 shared publications - Louis Gass
DMATH, University of Luxembourg, Esch-Sur-Alzette, Luxembourg
2 shared publications Francesca Pistolato
1 shared publication- Francesca Pistolato1 shared publication
- Giovanni Peccati
University of Luxembourg Luxembourg
1 shared publication
Latest Publications
- 2 February 2026
- Published by Elsevier in Journal of Geometry and Physics
- Vol. 223
Expected Lipschitz-Killing curvatures for spin random fields and other non-isotropic fields
- 2 February 2026
- Published by Elsevier in Journal of Geometry and Physics
- Vol. 223
Expected Lipschitz-Killing curvatures for spin random fields and other non-isotropic fields
- Open Access
Universal Cancellations in Uniform Random Waves
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 behavior of \emph{uniform random waves}, a much less studied non-Gaussian model in which the $L^2$ norm is constrained to be exactly equal to one in every realization (a normalization that is natural from the standpoint of quantum mechanics). We show that this norm-constrained formulation has deep consequences for the universality of the so-called \emph{Berry's cancellation phenomenon}, as well as for novel high-frequency asymptotic variance estimates. These effects manifest themselves in both local geometric functionals, such as the Lipschitz--Killing curvatures, and global ones, such as the number of connected components above a fixed threshold. A key byproduct of our analysis is a new explicit relation between Hermite expansions and spherical harmonic decompositions for $0$-homogeneous functionals of Gaussian vectors, which enables a systematic chaos-based analysis of non-Gaussian random waves.Open AccessUniversal Cancellations in Uniform Random Waves
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 behavior of \emph{uniform random waves}, a much less studied non-Gaussian model in which the $L^2$ norm is constrained to be exactly equal to one in every realization (a normalization that is natural from the standpoint of quantum mechanics). We show that this norm-constrained formulation has deep consequences for the universality of the so-called \emph{Berry's cancellation phenomenon}, as well as for novel high-frequency asymptotic variance estimates. These effects manifest themselves in both local geometric functionals, such as the Lipschitz--Killing curvatures, and global ones, such as the number of connected components above a fixed threshold. A key byproduct of our analysis is a new explicit relation between Hermite expansions and spherical harmonic decompositions for $0$-homogeneous functionals of Gaussian vectors, which enables a systematic chaos-based analysis of non-Gaussian random waves. - 21 March 2025
- Published by Springer Nature in Analysis and Mathematical Physics
- Vol. 15 (2) , 1-70
Geometry and topology of spin random fields
- 21 March 2025
- Published by Springer Nature in Analysis and Mathematical Physics
- Vol. 15 (2) , 1-70
Geometry and topology of spin random fields
- Top Cited Papers
- 2 April 2024
- Published by Springer Nature in Probability Theory and Related Fields
- Vol. 190 (3-4) , 1167-1197
The number of critical points of a Gaussian field: finiteness of moments
- 2 April 2024
- Published by Springer Nature in Probability Theory and Related Fields
- Vol. 190 (3-4) , 1167-1197
Top Cited PapersThe number of critical points of a Gaussian field: finiteness of moments
- 8 November 2022
- Published by American Mathematical Society (AMS) in Theory of Probability and Mathematical Statistics
- Vol. 107, 77-109
Isotropic random spin weighted functions on 𝑆² vs isotropic random fields on 𝑆³
We show that an isotropic random field on S U ( 2 ) SU(2) is not necessarily isotropic as a random field on S 3 S^3 , although the two spaces can be identified. The ambiguity is due to the fact that the notion of isotropy on a group and on a sphere are different, the latter being much stronger. We show that any isotropic random field on S 3 S^3 is necessarily a superposition of uncorrelated random harmonic homogeneous polynomials, such that the one of degree d d is necessarily a superposition of uncorrelated random spin weighted functions of every possible spin weight in the range { − d 2 , … , d 2 } \bigl \{-\frac {d}{2},\dots ,\frac {d}{2}\bigr \} , each of which is isotropic in the sense of S U ( 2 ) SU(2) . Moreover, for a random field of fixed degree, each spin weight appears with the same magnitude, in a sense to be specified. In addition we will give an overview of the theory of spin weighted functions and Wigner D D -matrices, with the purpose of gathering together many different points of view and adding ours. As a byproduct of this survey we will prove some new properties of the Wigner matrices and a formula relating the operators ð ð ¯ \eth \overline {\eth } and the horizontal Laplacian of the Hopf fibration S 3 → S 2 S^3\to S^2 , in the sense of [Bérard Bergery and Bourguignon, Illinois J. Math. 26 (1982), no. 2, 181–200.]
- 8 November 2022
- Published by American Mathematical Society (AMS) in Theory of Probability and Mathematical Statistics
- Vol. 107, 77-109
Isotropic random spin weighted functions on 𝑆² vs isotropic random fields on 𝑆³
We show that an isotropic random field on S U ( 2 ) SU(2) is not necessarily isotropic as a random field on S 3 S^3 , although the two spaces can be identified. The ambiguity is due to the fact that the notion of isotropy on a group and on a sphere are different, the latter being much stronger. We show that any isotropic random field on S 3 S^3 is necessarily a superposition of uncorrelated random harmonic homogeneous polynomials, such that the one of degree d d is necessarily a superposition of uncorrelated random spin weighted functions of every possible spin weight in the range { − d 2 , … , d 2 } \bigl \{-\frac {d}{2},\dots ,\frac {d}{2}\bigr \} , each of which is isotropic in the sense of S U ( 2 ) SU(2) . Moreover, for a random field of fixed degree, each spin weight appears with the same magnitude, in a sense to be specified. In addition we will give an overview of the theory of spin weighted functions and Wigner D D -matrices, with the purpose of gathering together many different points of view and adding ours. As a byproduct of this survey we will prove some new properties of the Wigner matrices and a formula relating the operators ð ð ¯ \eth \overline {\eth } and the horizontal Laplacian of the Hopf fibration S 3 → S 2 S^3\to S^2 , in the sense of [Bérard Bergery and Bourguignon, Illinois J. Math. 26 (1982), no. 2, 181–200.]
- 21 February 2022
- Published by Springer Nature in Analysis and Mathematical Physics
- Vol. 12 (2) , 1-64
Kac-Rice formula for transverse intersections
- 21 February 2022
- Published by Springer Nature in Analysis and Mathematical Physics
- Vol. 12 (2) , 1-64
Kac-Rice formula for transverse intersections
- Open Access
Differential Topology of Gaussian Random Fields
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) $X:M\to \mathbb{R}^k$, that we interpret as random variables with values in $\mathcal{C}^r(M, \mathbb{R}^k)$, inducing on it a Gaussian measure. When the latter is given the weak Whitney topology, the convergence in law of $X$ allows to compute the limit probability of certain events in terms of the probability distribution of the limit. This is true, in particular, for the events of a geometric or topological nature, like: "$X$ is transverse to $W$" or "$X^{-1}(0)$ is homeomorphic to $Z$". We relate the convergence in law of a sequence of GRFs with that of their covariance structures, proving that in the smooth case ($r=\infty$), the two conditions coincide, in analogy with what happens for finite dimensional Gaussian measures. We also show that this is false in the case of finite regularity ($r\in\mathbb{N}$), although the convergence of the covariance structures in the $\mathcal{C}^{r+2}$ sense is a sufficient condition for the convergence in law of the corresponding GRFs in the $\mathcal{C}^r$ sense. We complement this study by proving an important technical tools: an infinite dimensional, probabilistic version of the Thom transversality theorem, which ensures that, under some conditions on the support, the jet of a GRF is almost surely transverse to a given submanifold of the jet space.Open AccessDifferential Topology of Gaussian Random Fields
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) $X:M\to \mathbb{R}^k$, that we interpret as random variables with values in $\mathcal{C}^r(M, \mathbb{R}^k)$, inducing on it a Gaussian measure. When the latter is given the weak Whitney topology, the convergence in law of $X$ allows to compute the limit probability of certain events in terms of the probability distribution of the limit. This is true, in particular, for the events of a geometric or topological nature, like: "$X$ is transverse to $W$" or "$X^{-1}(0)$ is homeomorphic to $Z$". We relate the convergence in law of a sequence of GRFs with that of their covariance structures, proving that in the smooth case ($r=\infty$), the two conditions coincide, in analogy with what happens for finite dimensional Gaussian measures. We also show that this is false in the case of finite regularity ($r\in\mathbb{N}$), although the convergence of the covariance structures in the $\mathcal{C}^{r+2}$ sense is a sufficient condition for the convergence in law of the corresponding GRFs in the $\mathcal{C}^r$ sense. We complement this study by proving an important technical tools: an infinite dimensional, probabilistic version of the Thom transversality theorem, which ensures that, under some conditions on the support, the jet of a GRF is almost surely transverse to a given submanifold of the jet space.