Random walks and polymers in the presence of quenched disorder (Q861523)

This is a review paper about some random walk and polymer models in presence of quenched disorder. In random walk models (e.g., the Sinai random walk) the random walk trajectory is generated by local dynamical rules. In polymer models, instead, (e.g., wetting and pinning models, Poland-Scheraga model etc) to the polymer trajectory is associated a global Boltzmann weight. In all cases, one is interested in the situation where quenched (i.e., frozen) disorder is present. In the case of the Sinai model, disorder is present in that the probability that the walker jumps to the right rather than to the left when it is located at site \(n\) is a random variable \(\omega_n\), which depends on \(n\) but not on time. In the case of the wetting model, disorder is represented by ``charges'' placed on a one-dimensional region, which can attract or repel the polymer. Some interesting phenomena of the Sinai model (aging, anomalous diffusion, Golosov localization) and of pinning/wetting models (the occurrence of a localization/delocalization transition) are discussed. The paper is not intended to present rigorous results, but rather intuitive physical arguments (without details): in particular, there is a nice section (Section 2.1.4) on the strong disorder, renormalization group approach to dynamical localization in the Sinai walk, and one (Section 3.1) about the Harris criterion and the possibility of non-selfaveraging of extensive observables at the critical point, in presence of quenched randomness.