Lectures on the Brownian loop-soup: Lecture 1

In this mini-course, I will start by introducing the Brownian loop-soup and describing many of its basic properties. I will then explain the relation between the Brownian loop-soup and many other random objects in the plane such as restriction measures, Schramm-Loewner evolutions (SLE), Conformal loop ensembles (CLE), the Gaussian free field (GFF) and so on. These rich relations enable us to better understand the structure of the Brownian loop-soup. In particular, I will describe a series of results and open questions concerning the decomposition of Brownian loop-soup clusters.

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