Exploration processes of the Brownian half-plane
Vortrag von Fael Rebei
Sprecher eingeladen von: Prof. Dr. Jean Bertoin
Datum: 28.05.25 Zeit: 17.15 - 18.45 Raum: Y27H12
This project is an ongoing work with Armand Riera. The Brownian half-plane is a random surface that arises as the universal scaling limit in the Gromov-Hausdorff sense of large graphs embedded in the closed half-plane. We will present two exploration processes of this surface; the horohulls and the hulls, which correspond roughly to exploring it from a point at infinity, and from its root. We characterize the law of the horohulls, which in turn provides information on the local topology of the half-plane. We describe the joint law of the horohulls and the hulls, and support the idea that they are dual processes. Then, we exhibit a simple martingale which is a function of the hulls, which allows to define another surface whose law is absolutely continuous to whose of the Brownian half-plane. We show that this surface exhibits hyperbolic features, with some links to 3D non random geometry. We end with a few conjectures/open questions.