4 papers · 1 filter
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…
Growth-fragmentation processes in Brownian motion indexed by the Brownian tree
Jean-François Le Gall, Armand Riera
We consider the model of Brownian motion indexed by the Brownian tree. For every and every connected component of the set of points where Brownian motion is greater than…