16/04/2025, 17:00 — 18:00 — Online
Alejandro Rosales Ortiz, Universität Zürich, Switzerland
Excursion theory for Markov processes indexed by Lévy trees
We begin by introducing Markov processes indexed by Lévy trees, a notion which was developed in a series of works by Duquesne, Le Gall and Le Jan, and that has seen multiple applications in recent years. We will then present the main aspects of a theory, developed in two recent works with Armand Riera, that describes the evolution of a Markov process indexed by a Lévy tree between visits to a regular, instantaneous point of the state space. Despite the radically different setting, we will see that our results share strong similarities with the celebrated Itô excursion theory for Brownian motion. An excursion theory for Brownian motion indexed by the Brownian tree was previously developed by Le Gall and Abraham [JEMS;18], and in particular we recover their results by different methods. Our work is motivated by applications in random geometry.
