Speaker: Prof. Kilian Raschel (VIASM, CNRS)  

Time: 9:30-11:00  

Date: 16/10/2024  

Place: Room 201, Building C.  

Title: A functional equation approach to reflected Brownian motion
Abstract: The last two decades have seen a flurry of activity around the combinatorial model of walks in the quarter plane. One reason for this is that this model not only occupies a central position in enumerative combinatorics (via bijections with other combinatorial models), but it has also motivated different communities (probability, complex analysis, functional equations, Galois theory, etc.) to work together to develop new techniques and derive new results. While it can be said that walks in the quarter plane are now fairly well understood, a natural question for a probabilist is to study the continuous analogue, namely Brownian motion in a quadrant. It turns out that this model was introduced forty years ago using intrinsically probabilistic methods. In this talk I will explain how delicate probabilistic problems associated with Brownian motion in cones can be solved using functional equations, in particular Galois results on the nature of the solutions to such equations. This talk is based on work with several co-authors, mainly arXiv:2101.01562 and arXiv:2401.10734. No prior knowledge of Brownian motion is required.