Mercoledi' 24 Giugno, ore 14:30 Aula Picone, Dipartimento di Matematica (La Sapienza)
Seminario congiunto di Probabilita' (Roma1 e Roma 3)
Speaker: Vittoria Silvestri (Cambdrige)
Title: Fluctuation results for Hastings-Levitov planar growth
Abstract: In 1998 the physicists Hastings and Levitov introduced a family of continuum models to describe a range of physical phenomena of planar aggregation/diffusion. These consist of growing random clusters on the complex plane, which are built by iterated composition of random conformal maps. It was shown by Norris and Turner (2012) that in the case of i.i.d. maps the limiting shape of these clusters is a disc: in this talk I will show that the fluctuations around this shape are given by a random holomorphic Gaussian field F on {|z| > 1}, of which I will provide an explicit construction. When the cluster is allowed to grow indefinitely, I will show that the boundary values of F converge to a distribution-valued Fractional Gaussian Field on the unit circle, which is log-correlated, and critical in a sense that I will explain.
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Mercoledi' 24 Giugno, ore 15:30
Aula Picone, Dipartimento di Matematica (La Sapienza)
Seminario congiunto di Probabilita' (Roma1 e Roma 3)
Speaker: Oriane Blondel (Lione)
Title: Random walk on the East model (and other environments with spectral gap)
Abstract: The East model is a one-dimensional interacting particle system with non attractive spin-flip dynamics. In the physics literature, it is a key example of a model with glassy features. Here we take this model as a random environment and investigate the behaviour of a random walk whose jump rates depend on the current configuration. The analysis relies on general results established for random walks in random environment when the environment is Markovian with positive spectral gap.
Joint work with Luca Avena and Alessandra Faggionato.