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Multispecies asymmetric exclusion processes (ASEPs) are interacting particle systems characterised by simple, local dynamics, where particles occupy lattice sites and interact only with their adjacent neighbors, following asymmetric exchange rules based on their species labels. I will present recent results on two-point correlation functions in multispecies ASEPs, including models on finite rings and their continuous-space limit as the number of sites tends to infinity. Using combinatorial tools such as Ferrari–Martin multiline queues, projection techniques, and bijective arguments, we derive exact formulas for adjacent particle correlations and resolve a conjecture in the continuous multispecies TASEP (Aas and Linusson, AIHPD 2018). We also extend finite-ring results of Ayyer and Linusson (Trans AMS, 2017) to the partially asymmetric case (PASEP), formulating new correlation functions that depend on the asymmetry parameter. I will briefly outline ongoing work on boundary-driven multispecies B-TASEP and long-time limiting states in periodic ASEPs, suggesting connections between pairwise correlations and stationary-state structure.

Das Beweisen ist für die Mathematik als Disziplin von zentraler Bedeutung und spielt daher auch in der mathematischen Ausbildung eine wichtige Rolle. Lernende sollen die Mathematik als deduktives System begreifen, die Art der Absicherung mathematischer Ergebnisse verstehen, argumentative Herausforderungen erfolgreich bewältigen können und so ein adäquates Verständnis von mathematischen Beweisen aufbauen. Ausgehend von einem theoretischen Rahmenmodell zum mathematischen Beweisverständnis werden Ergebnisse empirischer Studien vorgestellt, die das Beweisverständnis von Lernenden in unterschiedlichen Phasen der mathematischen Ausbildung untersuchen und Möglichkeiten der Förderung aufzeigen. ______________________ Invited by Prof. Stefan Ufer

We study opportunistic traders that try to detect and exploit the order flow of dealers hedging their net exposure to the FX fix. We also discuss how dealers can take this into account to balance not only risk and trading costs but also information leakage in an appropriate manner. It turns out that information leakage significantly expands the set of scenarios where both dealers and the clients whose orders they execute benefit from hedging part of the exposure before the fixing window itself. (Joint work in progress with Roel Oomen (Deutsche Bank) and Mateo Rodriguez Polo (ETH Zurich))

The exact treatment of Markovian models on complex networks requires knowledge of probability distributions expo- nentially large in the number of nodes n. Mean-field approximations provide an effective reduction in complexity of the models, requiring only a number of phase space variables polynomial in system size. However, this comes at the cost of losing accuracy close to critical points in the systems dynamics and an inability to capture correlations in the system. In this talk, we introduce a tunable approximation scheme for Markovian spreading models on networks based on matrix product states (MPSs). By controlling the bond dimensions of the MPS, we can investigate the effective dimensional- ity needed to accurately represent the exact 2n dimensional steady-state distribution. We introduce the entanglement entropy as a measure of the compressibility of the system and find that it peaks just after the phase transition on the disordered side, in line with the intuition that more complex states are at the ’edge of chaos’. The MPS provides a systematic way to tune the accuracy of the approximation by reducing the dimensionality of the systems state vector, leading to an improvement over second-order mean-field approximations for sufficiently large bond dimensions.