Mini courses 

In my lectures I will discuss the basic theory of the Brownian web, some of its applications, and more recent developments. The plan for the lectures is:

Lecture 1: The Brownian web; Convergence of systems of nearest-neighbour coalescing random walks to the Brownian web, structure of the Brownian web including special points, and an application to the Arratia flow.

Lecture 2: Applications of the Brownian web; The true self-repelling motion, the directed spanning forest, the Brownian castle, and the Brownian marble.

Lecture 3: The Brownian net; Equivalent definitions and applications to voter model perturbations and Howitt-Warren flows.

Lecture 4: Universality of the Brownian web; Convergence of non-nearest neighbour coalescing random walks to the Brownian web, the augmented Brownian web, and multi-scale webs.

Link for the mini course notes: https://staff.utia.cas.cz/swart/lecture_notes/Brownian_web26_07_14.pdf