*** Apologies for cross-posting ***   Dear Colleagues, we would like to invite you to the following Probability seminar that will take place at the Department of Mathematics, University of Padova, on January 14. ____________________________________________________________________________________________________ DR. RICHARD C. KRAAIJ (Delft University of Technology) “Large deviations for weakly coupled slow-fast systems via the comparison principle of an associated Hamilton-Jacobi equation” 14 JANUARY (Tuesday), 11:00; ROOM 1BC50, Dipartimento di Matematica “Tullio Levi-Civita”, Via Trieste 63, Padova ABSTRACT. In statistical physics many interesting phenomena, e.g. behavior of systems at critical parameters or in the theory of hydrodynamic limits, arise from systems having multiple time-scales. A slow component is influenced by fast components, and as the number of interacting components tends to infinity, limiting results for the slow component are obtained in terms of `averaged' versions of the fast components. I will consider in my talk the fluctuations (large deviations) of coupled Markovian systems with two-time scales. These fluctuations can arise from two sources: fluctuations of the slow process itself, or fluctuations of the large time averages of the fast process, effectively leading to a competition of two fluctuation effects. To obtain the large deviation principle, we consider an associated Hamilton-Jacobi-Bellman equation of which the Hamiltonian is given in terms of the two fluctuation effects. We establish under mild conditions that this Hamilton-Jacobi-Bellman equation is well-posed, and as a consequence that we have a large deviation principle for a wide class of weakly coupled Markov processes. Based on joint work with Mikola Schlottke (Eindhoven, The Netherlands). ____________________________________________________________________________________________________ All of you are very welcome. Best regards, Francesca Collet