Dear Colleagues, we would like to invite you to the following seminars by Luisa Andreis (Università di Firenze) and Giulia Carigi (University of Reading) to be held Wednesday, May 18th, at Dipartimento di Matematica in Pisa and online via Google Meets.
The organizers, A. Agazzi and F. Grotto
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Location: Sala Seminari, Dipartimento di Matematica, Pisa Google Meet Link: https://meet.google.com/gji-phwo-vbg
Time: May 18th, 2022, 14:00-15:00 CET Speaker: Luisa Andreis (UniFi) Title:Large deviations for coagulation processes: an approach via graphs Abstract: Interacting particle systems where particles interact via coagulation are of great interest for their various behaviours. In particular, interesting phenomena can occur, depending on the structure of the kernel which is giving a rate to each coagulation. Among these phenomena there is the famous phase transition that goes under the name of gelation, i.e. the appearance of one (or multiple) giant particle(s). Although fluid limits are known for the rescaled version of stochastic coagulation processes (convergence to the Smoluchowski coagulation equation and its modification), very few is known about large deviations and rare events in this framework. In this talk we will explore some connections of these processes with random graphs and how to use this connection to attack the problem of studying large deviations. This also allows a comparison with the phase transition in graphs, where a giant component appears. Some remarks about the possible generalization to coagulation kernels that depend on spatial position will be given. This is based on ongoing joint works with Wolfgang K ̈onig (WIAS and TU Berlin), Tejas Iyer (WIAS), Heide Langhammer (WIAS), Elena Magnanini (WIAS) and Robert Patterson (WIAS).
Time: May 18th, 2022, 15:00-16:00 CET Speaker: Giulia Carigi (University of Reading) Title: Ergodic properties for a stochastic two-layer model of geophysical fluid dynamics Abstract: A two-layer quasi-geostrophic model for geophysical flows is studied, with the upper layer being perturbed by additive noise. This model is popular in the geosciences, for instance to study the effects of a stochastic wind forcing on the ocean. A rigorous mathematical analysis however meets with the challenge that the noise configuration is spatially degenerate as the stochastic forcing acts only on the top layer. Exponential convergence of solutions laws is established, implying a spectral gap of the associated Markov semigroup on a space of Hölder continuous functions. Moreover, response theory with respect to changes in the average wind forcing is established. Specifically, it is shown that the averages of a class of observables against the invariant measure are differentiable (linear response) and locally Hölder continuous (fractional response) as functions of a deterministic additive forcing. In doing so, a framework suitable to establish (linear and fractional) response for a class of nonlinear stochastic partial differential equations is provided.