Seminars on “Extreme value theory for  dynamical systems” and “Scaling limit of an exclusion process with Vorticity”

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​Title: Extreme value theory for  dynamical systems ​

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Abstract: Extremes are related to high impact and serious hazard events and hence their study and prediction has been and continue to be highly relevant for all kind of applications in geoscience and beyond. In the last fifteen years the classical extreme value theory for stochastic processes has been extended to  dynamical systems. We will review the relation between the parameters of the extreme distributions and invariants of the underlying dynamical system if it is uniformly hyperbolic. Modulation of external factor (climate change as an obvious example) have an impact on extremes and their properties. We explore whether there exists a linear response theory for extremes.​

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Time: 15.30​

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Speaker: Leonardo De Carlo​

CAMGSD, Istituto Superior Tecnico de Lisboa​

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Abstract: Interacting particles systems that are gradient, i.e. where the microscopic current can be computed as gradient, are proved to have a nonlinear​ diffusion equation with a symmetric diffusion matrix. Here we show that the picture is more general. Superimposing to the simple exclusion process some​ turbolent dynamics, i.e. models where the microscopic current can be computed as a discrete curl, we prove that the diffusion matrix in the Fick’s law​ for the macroscopic current now it is given as the sum of a symmetric matrix and an antisymmetric one. For these kind of systems, we get the same diffusion hydrodynamics of its non-turbolent version because the new part of the macroscopic current has zero net contribution to the PDE. Joint work with D. Gabrielli and P. Goncalves​