Dear colleagues,

We are happy to announce the following online talk:

Speaker: *Guangqu Zheng* (University of Kansas)

Title: *Malliavin derivatives of hyperbolic Anderson model with applications to its absolute continuity and spatial averages.*

Date and time: *Monday May 10, 17:30-18:30 (Rome time zone)*

Abstract: see below.

Zoom link: https://us02web.zoom.us/j/83843864962?pwd=NlNadHhIRkdzYUErZWJpbTNJaytDUT09 Meeting ID: 838 4386 4962 Passcode: 5gVVXb

This talk is the second of the *(PMS)^2: Pavia-Milano Seminar series on Probability and Mathematical Statistics* organized jointly by the universities Milano-Bicocca, Pavia, Milano-Politecnico and Milano-Statale.

Participation is free and welcome! (though limited to 100 participants for technical reasons)

Best regards The organizers (Mario Maurelli, Carlo Orrieri, Maurizia Rossi, Margherita Zanella)

*Abstract:* In this talk, we present recent work on the hyperbolic Anderson model driven by a space-time colored Gaussian homogeneous noise with spatial dimension one and two. Under mild assumptions, we provide Lp-estimates of the iterated Malliavin derivatives of the solution in terms of the fundamental solution of the wave solution. We present two applications: (1) We present quantitative central limit theorems for spatial averages of the solution to the hyperbolic Anderson model, where the rates of convergence are described by the total variation distance. These quantitative results have been elusive so far due to the temporal correlation of the noise blocking us from using the Itô calculus. (2) We establish the absolute continuity of the law for the hyperbolic Anderson model. The Lp-estimates of Malliavin derivatives are crucial ingredients to verify a local version of Bouleau-Hirsch criterion for absolute continuity. Our approach substantially simplifies the arguments for the one-dimensional case, which has been studied in the recent work by Balan, Quer-Sardanyons and Song (2019). This talk is based on the joint work (arXiv:2101.10957) with *R. Balan*, *D. Nualart* and *L. Quer-Sardanyons* (2021).

- - - Maurizia Rossi

Dipartimento di Matematica e Applicazioni Università di Milano-Bicocca