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04.02.2019 16:15 Sarah Loos (TU Berlin):
Stochastic systems with time delay – Fokker-Planck approach, Markovian embedding and thermodynamic notionsMI 03.06.011 (Boltzmannstr. 3, 85748 Garching)

A discrete time delay in the Langevin equation naturally leads to an infinite hierarchy of Fokker- Planck (FP) equations for the n-time joint probability distribution functions [1,2]. Finding a probabilistic description is hence challenging, especially for systems subject to nonlinear forces. One major issue is that the higher members of the hierarchy contain unknown functional derivatives between noise and the stochastic state variable. In this talk, I will introduce a new way to derive the Fokker-Planck equation via a Markovian embedding technique. In particular, I will discuss an extended Markovian system with auxiliary variables which generates the same dynamics as the original (delayed) system in the limit of an infinitely large system. This extended system can be studied under a (stochastic) thermodynamical [3] perspective, allowing to find a closed expression for the entropy production, which is a nontrivial problem in the presence of delay [4]. [1] S. Guillouzic et al., PRE 59, 3970 (1999). [2] S. A. M. Loos and S. H. L. Klapp, PRE 96, 012106 (2017). [3] S. A. M. Loos and S. H. L. Klapp, arXiv:1806.04995 (2017). [4] M. L. Rosinberg, T. Munakata, and G. Tarjus, PRE 91, 042114 (2015).

S. A. M. Loos and S. H. L. Klapp

04.02.2019 16:30 Thomas Beekenkamp (LMU) :
Sharpness of the Percolation Phase Transition for the Contact Process on Z^dB 252 (Theresienstr. 39, 80333 München)

The contact process is a model for the spread of infection on a graph. Each vertex of Z^d is either healthy or infected. Infected vertices become healthy with rate 1, independent of the rest of the process. Healthy sites become infected with a rate of lambda times the number of neighbours that are infected, where lambda is the parameter of the model. There exists a critical value for lambda above which there exists an infinite cluster and below which all clusters are finite. We show that this phase transition is sharp, i.e., below this critical value all clusters are exponentially small. The proof draws on a series of recent papers by Duminil-Copin, Raoufi and Tassion in which they prove sharp phase transitions for a variety of models using the OSSS inequality.

06.02.2019 14:30 Clotilde Fermanian Kammerer (Université Paris Est - Créteil Val de Marne/TUM JvN):
Microlocal interludeMI HS 3 (Boltzmannstr. 3, 85748 Garching)

Some questions are at the threshold between harmonic analysis and partial differential equations and can be studied in the Euclidean space or in more complicated non-commutative settings like compact Lie groups such as the Heisenberg group. Our goal will be to use one of these questions in order to get familiar with the microlocal approach and to understand how it can be implemented in various frameworks.

07.02.2019 15:45 Mikaela Iacobelli (Durham University):
From quantization of measures to very fast diffusion equationsMI 03.08.011 (Boltzmannstr. 3, 85748 Garching)

In this talk I would like to present some recent results on the asymptotic behaviour of a very fast diffusion PDE. This equation is motivated by the gradient flow approach to the problem of quantization of measures. I will present a work in progress with Francesco Saverio Patacchini and Filippo Santambrogio where we use the JKO scheme to obtain existence, uniqueness and exponential convergence to equilibrium under minimal assumptions on the data.

07.02.2019 17:15 David Gontier (CEREMADE, Université Paris-Dauphine):
Symmetry breaking in the Hartree-Fock jelliumMI 03.08.011 (Boltzmannstr. 3, 85748 Garching)

In this talk, we present two types of symmetry breakings that occur respectively in the Hartree-Fock jellium, and in the free fermionic gas. We first discuss the Overhauser's spatial symmetry breaking in the HF jellium, and give a lower bound on the energy gain due to this symmetry breaking. Then we focus on the free gas, and we present the phase diagram of the spin-polarisation of the gas at different densities and different temperatures. This is joint work with Mathieu Lewin and Christian Hainzl.