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math.PR2024
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…
math.PR2024
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…
math.PR2024
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.…