7 papers
Peeling the Brownian half-plane
Jean-François Le Gall, Armand Riera
We establish a new spatial Markov property of the Brownian half-plane. According to this property, if one removes a hull centered at a boundary point, the remaining space equipped…
Spatial Markov property in Brownian disks
Jean-François Le Gall, Armand Riera
We derive a new representation of the Brownian disk in terms of a forest of labeled trees, where labels correspond to distances from a subset of the boundary. We then use this repr…
The structure of the local time of Markov processes indexed by Levy trees
Armand Riera, Alejandro Rosales-Ortiz
We construct the analogue of the local time -- at a fixed point -- for Markov processes indexed by Levy trees. We start by proving that Markov processes indexed by Levy trees s…
Isoperimetric inequalities in the Brownian plane
Armand Riera
We consider the model of the Brownian plane, which is a pointed non-compact random metric space with the topology of the complex plane. The Brownian plane can be obtained as the sc…
Spine representations for non-compact models of random geometry
Jean-François Le Gall, Armand Riera
We provide a unified approach to the three main non-compact models of random geometry, namely the Brownian plane, the infinite-volume Brownian disk, and the Brownian half-plane. Th…
Some explicit distributions for Brownian motion indexed by the Brownian tree
Jean-François Le Gall, Armand Riera
We derive several explicit distributions of functionals of Brownian motion indexed by the Brownian tree. In particular, we give a direct proof of a result of Bousquet-Mélou and Jan…