5 papers
Time-inhomogeneous N-particle Branching Brownian Motion and the continuous random energy model
Alexandre Legrand, Pascal Maillard
The -particle branching Brownian motion (-BBM) is a branching Markov process which describes the evolution of a population of particles undergoing reproduction and selection.…
The localized phase of pinning models with correlated Gaussian disorder
Giambattista Giacomin, Alexandre Legrand, Marco Zamparo
We show that most of the results proven in the localized regime of the pinning model with independent disorder (notably, regularity of the free energy, size of…
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…
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…
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, co…