Brownian web appears as the scaling limit of coalescing simple symmetric random walks starting from every point on the oriented lattice. Heuristically, it can be described as coalescing Brownian motions starting from everywhere on the space-time plane of \(\mathbb{R}^2\). However, one needs to make this heuristics rigorous. Fontes et. al. suggested a topology such that the Brownian web can be described using countably many coalescing Brownian motions and it can be treated as a random variable taking values in a Polish space. Since the introduction of this topological setup, convergence to the Brownian web has been extensively studied for many models. Some variants of Brownian web also have been constructed such as, the Brownian net and the dynamic Brownian web. Convergence questions to these variants have been less explored and many aspects are still open.
In this talk I will discuss the proposed topology of convergence (constructed by Fontes et. al.) and convergence questions too. I will briefly describe different variants of the Brownian web. Towards the end we will discuss the newly introduced spatial tree topology, introduced by Martin Hairer et. al., for the Brownian web.
• I will not assume any prior knowledge of Brownian web. Review of Donsker's invariance principle could be helpful.
• Lecture 1: September 22, 5:00 PM -- 5:50 PM
• Lecture 2: September 23, 5:00 PM -- 5:50 PM
••••• September 24, 2026 is not scheduled •••••
• Lecture 3: September 25, 3:00 PM -- 3:50 PM (Please note the change in time for the third lecture.)
