CS07: Stochastic properties of time-dependent random fields

date: 7/15/2025, time: 14:00-15:30, room: IM 601

Organizer: Anna Vidotto (Sapienza University of Rome)

Chair: Anna Vidotto (Sapienza University of Rome)

Quantitative Gaussian approximation for the non-linearity parameter estimator in perturbed random fields

Claudio Durastanti (Sapienza University of Rome)

The nonlinearity parameter \(f_{\operatorname{NL}}\) plays a pivotal role in modern cosmology, quantifying the amplitude of primordial non-Gaussianity in the cosmic microwave background (CMB) temperature fluctuations. While the simplest inflationary models predict nearly Gaussian fluctuations, more sophisticated scenarios can give rise to measurable non-Gaussian features. In particular, the local model of non-Gaussianity introduces a quadratic correction to an underlying Gaussian field, leading to non-trivial three-point correlations encapsulated by the CMB bispectrum. To estimate \(f_{\operatorname{NL}}\) efficiently, Komatsu, Spergel, and Wandelt introduced a class of statistically optimal and computationally tractable estimators—now known as KSW estimators—that exploit spherical harmonic decompositions and rotational invariance through Wigner-3j symbols. In this paper, we study KSW-like estimators, establishing a quantitative central limit theorem (CLT) by applying fourth-moment theorems from Wiener chaos theory. Our analysis demonstrates asymptotic normality for this class of estimators and provides explicit convergence rates in terms of the decay of fourth cumulants.

Statistical inference for cylindrical processes on the sphere

Radomyra Shevchenko (Université Côte d’Azur / Centrale Méditerranée)

In this talk, I will present a parameter estimation method for time-dependent random fields on the unit sphere, with a particular focus on the spherical fractional Brownian motion defined as a cylindrical process with respect to the spherical harmonics. I will introduce a Hurst parameter estimator based on quadratic variations computed along a single geodesic line in space, using observations at two time points, and discuss its asymptotic properties.

Limit theorems for spatiotemporal functionals of Gaussian fields

Leonardo Maini (Università di Roma Tor Vergata)

Our study focuses on limit theorems for spatiotemporal functionals of Gaussian fields, with a particular emphasis on the differences between the separable case, where the covariance structure is a tensor product of the spatial and temporal covariances, and the Gneiting class. Specifically, we highlight the assumptions required to derive a central or non-central limit theorem for these functionals. This work is based on a recent publication and ongoing research with N. Leonenko, I. Nourdin and F. Pistolato.