Strong disorder in semidirected random polymers. (English. French summary) Zbl 1290.82013

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.


82B41 Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics
82B44 Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics
60G50 Sums of independent random variables; random walks
82D60 Statistical mechanics of polymers
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