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.
Reviewer: Farruh Mukhamedov (Kuantan)
MSC:
| 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 |
Keywords:
random walks;random potential;Lyapunov norms;strong disorder;localization;fractional momentsCite
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