## View abstract

### Session S04 - Random Walks and Related Topics

Thursday, July 15, 14:20 ~ 14:50 UTC-3

## Extremal distance and conformal radius of a $CLE(4)$ loop

### Avelio Sepúlveda

In this talk, we will discuss the geometry of the loop of a $CLE(4)$ surrounding the origin. In particular, we show how to compute the joint law between the conformal radius seen from the origin of the domain surrounded by the loop together with the extremal distance from this loop to the boundary. This joint law is related to certain random times of the Brownian motion, more precisely the first exit time of the set $[-2\pi, 2\pi]$ together with the last hit of $0$. We will explain where this relationship comes from together with a new characterization of this coupling.