Tree structures are ubiquitous in nature, and it is natural to want to model trees which are somehow randomly generated. In mathematics, we think of trees as connected graphs (or networks) with no cycles; these are a fundamental object of study in combinatorics.
In this talk, I will discuss a simple model of random trees, and what we can say about large instances of these trees. Along the way, we will encounter several beautiful bits of combinatorics and probability, including Cayley’s formula, Galton-Watson branching processes, the Central Limit Theorem, random walks, Brownian motion and Poisson processes. My aim is that the talk should be accessible to everyone who has attended the first-year probability course (as long as they are willing to take a few things on trust!).