Termine Angewandte Mathematik Münster

The exclusion process is one of the best-studied examples of an interacting particle system. In this talk, we consider the stationary distribution of asymmetric simple exclusion processes with open boundaries. We project the stationary distribution onto a subinterval, whose size is allowed to grow with the length of the underlying segment. Depending on the boundary parameters for the exclusion process, we provide sufficient conditions such that the projected stationary distribution is close in total variation distance to a product measure. This talk is based on joint work with Evita Nestoridi.

To tackle parametric partial differential equations with highly heterogeneous coefficients, we propose an adaptive localized basis construction procedure based on both offline training and online enrichment. First, in the offline phase, a set of problem-adapted local basis functions is precomputed. Next, in the online phase, we use a localized residual-based a posteriori error estimator to investigate the accuracy of the reduced solution for any given new parameter. As the error estimator is localized, we can exploit it to adaptively enrich the reduced solution space locally where needed. The approach thus guarantees the accuracy of reduced solutions given any possibly insufficient reduced basis that was constructed during the offline phase. Numerical experiments demonstrate the efficiency of the proposed method.

The 2d (massless) Sinh-Gordon model is amongst the simplest 2d quantum field theories that are expected to be integrable (= infinitely many symmetries), but without conformal symmetry. In this talk I will explain a rigorous construction of this model and its vertex correlations (= Laplace transforms) on the infinite cylinder using probability theory. In particular, I will explain how the theory of Gaussian multiplicative chaos can be used to analyze the spectrum of the corresponding Sinh-Gordon Hamiltonian. This talk will be based on joint work with Colin Guillarmou and Vincent Vargas.

We study the (discrete) Phi^4 model on Z^d with algebraically decaying long-range interactions. This model is the natural discrete analogue of the fractional continuous Phi^4 model. We first describe some general properties of the phase transition that the model undergoes. Then, we study the nature of the critical scaling limits of the model, proving in particular the (marginal) triviality of these limits in dimension 3 with well-chosen interactions.