Oberseminar Wahrscheinlichkeitstheorie
Joint research seminar of LMU and TUM in Probability Theory
Students and guests welcome.
Organizers:
Noam
Berger (TUM),
Nina
Gantert
(TUM),
Konstantinos Panagiotou (LMU),
Markus
Heydenreich (LMU),
Sabine
Jansen (LMU),
Franz Merkl
(LMU),
Silke
Rolles (TUM)
Upcoming talks:
| Mon 7 Jul 2025, 16:30: Nimisha Pahuja Multispecies asymmetric exclusion processes: correlations and limiting behaviours |
| 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. |
| Parkring 11, Garching-Hochbrück. |
| Mon 21 Jul 2025, 16:30: Mykhaylo Shkolnikov Cascade equation in the Stefan problem and equilibria of mean field games |
| After motivating the Stefan problem from the random growth model perspective, I will discuss its discontinuities in time. These turn out to be characterized by the cascade equation, a second-order hyperbolic PDE. Questions of existence and regularity for the latter can be answered by expressing its solution as the value function of a player in an equilibrium of a suitable mean field game. Based on joint work with Yucheng Guo and Sergey Nadtochiy. |
| Parkring 11, Garching-Hochbrück. Room BC1 2.01.10 (8101.02.110) |