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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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.