5 papers
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…
Phase transition in the Integrated Density of States of the Anderson model arising from a supersymmetric sigma model
Margherita Disertori, Valentin Rapenne, Constanza Rojas-Molina +1
We study the Integrated Density of States (IDS) of the random Schrödinger operator appearing in the study of certain reinforced random processes in connection with a supersymmetric…
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…