Strong disorder in semidirected random polymers (Q372564)

The present paper is devoted to a random walk in a random potential, which models a situation of a random polymer. The annealed and quenched costs to perform long crossings from a point to a hyperplane are studied. Note that the distribution of the random polymer is given by the Gibbs measure related to the walk. These costs are measured by the so-called Lyapunov norms. One of the main results of the paper is the identification of situations where the point-to-hyperplane annealed and quenched Lyapunov norms are different. Moreover, it is proved that in these cases the polymer path exhibits localization.