Research

I mainly work on the edge reinforced random walk and the vertex reinforced jump process, this is a topic in the intersection of

• sigma model / statistical mechanics,
• self interacting random process,
• random Schrodinger operators.

My general research interests are probability, statistical mechanics, mathematical physics and their applications.

Publications and preprints

1. A multi-dimensional version of Lamperti’s relation and the Matsumoto-Yor opposite drift theorem (Joint with T. Gerard, C. Sabot) Arxiv 2004

2. On $H^{2|2}$ Isomorphism theorems and reinforced loop soup (Joint with Y. Chang, DZ. Liu) Arxiv 1911

3. A note on recurrence of the Vertex reinforced jump process and fractional moments localization. (joint with A. Collevecchio) Electronic Journal of Probability

4. Hitting times of interacting drifted Brownian motions and the vertex reinforced jump process (joint with C. Sabot) Annals of Probability

5. Speed of Vertex reinforced jump process on Galton-Watson trees (joint with X. Chen Journal of Theoretical Probability)

6. A random Schrödinger operator associated with the Vertex Reinforced Jump Process on infinite graphs (joint with C. Sabot) Journal of the AMS

7. The Vertex Reinforced Jump Process and a Random Schrödinger operator on finite graphs.(joint with C. Sabot, P. Tarrès, Annals of Probability)

8. How Vertex reinforced jump process arises naturally. (Annales de l’institut Henri Poincaré)

9. A Russo Seymour Welsh Theorem for critical site percolation on $\mathbb{Z}^2$ (Master thesis) http://arxiv.org/abs/1309.2273