4 papers · 1 filter
A continuous random operator associated with the Vertex Reinforced Jump Process on the circle and the real line
V Rapenne, C Sabot
In this paper, we focus on the scaling-limit of the random potential associated with the Vertex Reinforced Jump Process (VRJP) on one-dimensional graphs. Moreover, we give a fe…
A multi-dimensional version of Lamperti's relation and the Matsumoto-Yor processes
Thomas Gérard, Valentin Rapenne, Christophe Sabot +1
This paper presents a multidimensional extension of the Matsumoto-Yor properties related to exponential functionals of drifted Brownian motion. The extension involves the interacti…
About the asymptotic behaviour of the martingale associated with the Vertex Reinforced Jump Process on trees and Z d
Valentin Rapenne
We study the asymptotic behaviour of the martingale ( n (o)) nN associated with the Vertex Reinforced Jump Process (VRJP). We show that it is bounded in L p for every p > 1…
Invariant measures of critical branching random walks in high dimension
Valentin Rapenne
In this work, we characterize cluster-invariant point processes for critical branching spatial processes on R d for all large enough d when the motion law is -stable or has a fi…