14 citations · 57 across the 17 of their papers we have counts for
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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…
A multi-dimensional version of Lamperti's relation and the Matsumoto-Yor opposite drift theorem
Thomas Gerard, Christophe Sabot, Xiaolin Zeng
A classic result on the 1-dimensional Brownian motion shows that conditionally on its first hitting time of 0, it has the distribution of a 3-dimensional Bessel bridge. By applying…
On Isomorphism theorems and reinforced loop soup
Yinshan Chang, Dang-Zheng Liu, Xiaolin Zeng
We show that supersymmetric (susy) hyperbolic isomorphism theorems that relate Vertex Reinforced Jump Processes and field, introduced in [2] and [3], are annealed version…
A note on recurrence of the Vertex reinforced jump process and fractional moments localization
Andrea Collevecchio, Xiaolin Zeng
We give a simple proof for recurrence of vertex reinforced jump process on \(\mathbb{Z}^d\), under strong reinforcement. Moreover, we show how the previous result implies that line…
Hitting times of interacting drifted Brownian motions and the vertex reinforced jump process
Christophe Sabot, Xiaolin Zeng
Consider a negatively drifted one dimensional Brownian motion starting at positive initial position, its first hitting time to 0 has the inverse Gaussian law. Moreover, conditional…
Speed of Vertex reinforced jump process on Galton-Watson trees
Xinxin Chen, Xiaolin Zeng
We give an alternative proof of the fact that the vertex reinforced jump process on Galton- Watson tree has a phase transition between recurrence and transience as a function of c,…
A random Schrödinger operator associated with the Vertex Reinforced Jump Process on infinite graphs
Christophe Sabot, Xiaolin Zeng
This paper concerns the Vertex reinforced jump process (VRJP), the Edge reinforced random walk (ERRW) and their link with a random Schrödinger operator. On infinite graphs, we defi…
The Vertex Reinforced Jump Process and a Random Schrödinger operator on finite graphs
Christophe Sabot, Pierre Tarrès, Xiaolin Zeng
We introduce a new exponential family of probability distributions, which can be viewed as a multivariate generalization of the Inverse Gaussian distribution. Considered as the pot…
How Vertex reinforced jump process arises naturally
Xiaolin Zeng
We prove that the only nearest neighbor jump process with local dependence on the occupation times satisfying the partial exchangeability property is the vertex reinforced jump pro…
A Russo Seymour Welsh Theorem for critical site percolation on \(\mathbb{Z}^2\)
Xiaolin Zeng
The Russo-Seymour-Welsh Theorem for Z^2 bond or T (triangular lattice) site percolation states that at criticality, for all fixed real λ, the probability of the existence of a hori…