4 papers
The localized phase of pinning models with correlated Gaussian disorder
Giambattista Giacomin, Alexandre Legrand, Marco Zamparo
We demonstrate that the results established for the localized regime of the pinning model with independent disorder -- notably the regularity of the free energ…
A random polymer approach to the weak disorder phase of the vertex reinforced jump process
Quentin Berger, Alexandre Legrand, Rémy Poudevigne +1
In this paper, we study the transient phase of the Vertex Reinforced Jump Process (VRJP) in dimension . In Sabot, Zeng (2019), the authors introduce a positive martingale…
Some FKG inequalities for stochastic processes
Alexandre Legrand
This paper is interested in proving correlation inequalities of the FKG-type for various stochastic processes in continuous time. The pivotal tool which yields these correlation in…
Recurrence and transience of the critical random walk snake in random conductances
Alexandre Legrand, Christophe Sabot, Bruno Schapira
In this paper we study the recurrence and transience of the -valued branching random walk in random environment indexed by a critical Bienaymé-Galton-Watson tree, con…