14 citations · 57 across the 17 of their papers we have counts for
17 papers
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…
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…
On -convex compactness in random locally convex modules
Mingzhi Wu, Xiaolin Zeng, Shien Zhao
For the study of some typical problems in finance and economics, Žitković %[G. Žitković, Convex compactness and its applications, Math. Finan. Eco., 3(1)(2010) 1--12] introduced co…
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…
On random convex analysis
Tiexin Guo, Erxin Zhang, Mingzhi Wu +3
Recently, based on the idea of randomizing space theory, random convex analysis has been being developed in order to deal with the corresponding problems in random environments suc…
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,…
Some results on the Orlicz space generated from a random normed module
Mingzhi Wu, Long Long, Xiaolin Zeng
Noting the important role the abstract space has played in the development of random normed modules, in this paper we introduce and study the Orlicz space generated from a ra…
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…
Random convex analysis (I): separation and Fenchel-Moreau duality in random locally convex modules
Tiexin Guo, Shien Zhao, Xiaolin Zeng
To provide a solid analytic foundation for the module approach to conditional risk measures, our purpose is to establish a complete random convex analysis over random locally conve…
Random convex analysis (II): continuity and subdifferentiability theorems in --pre--barreled random locally convex modules
Tiexin Guo, Shien Zhao, Xiaolin Zeng
In this paper, we continue to study random convex analysis. First, we introduce the notion of an --pre--barreled module. Then, we develop the theory of random duality under th…
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…
On random convex analysis -- the analytic foundation of the module approach to conditional risk measures
Tiexin Guo, Shien Zhao, Xiaolin Zeng
To provide a solid analytic foundation for the module approach to conditional risk measures, this paper establishes a complete random convex analysis over random locally convex mod…