Xiangyu Cao (ENS Paris)
Clusters in branching processes
Branching Brownian motion and its long-range generalisations are simple models of a variety of catastrophic phenomena, such as epidemic spreading and avalanches. Despite the simplicity of these models, they generate interesting geometric structures, in particular, clusters. I will discuss a simple method to count clusters and characterise their spatial separation, which turn out to be governed by nontrivial critical exponents. As an application, I will test the theory against real-world data generated by a famous recent epidemic outbreak.