title: Crossing probability for directed polymers in random media.
abstract: We study the probability that two directed polymers in the same random potential do not intersect. We use the replica method to map the problem onto the attractive Lieb-Liniger model with generalized statistics between particles. Employing both the nested Bethe ansatz and known formula from MacDonald processes, we obtain analytical expressions for the first few moments of this probability and compare them to a numerical simulation of a discrete model at high temperature. From these observations, several large time properties of the noncrossing probabilities are conjectured. Extensions of our formalism to more general observables are discussed.
authors.affiliation: Laboratoire de Physique Théorique et Modèles Statistiques (UMR CNRS 8626), Université Paris-Sud, Orsay, France.
authors.forename: Andrea
authors.initials: A
authors.lastname: De Luca
authors.affiliation: Laboratoire de Physique Théorique de l'ENS, CNRS and Ecole Normale Supérieure de Paris, Paris, France.
authors.forename: Pierre
authors.initials: P
authors.lastname: Le Doussal