07-244 Dmitry Ioffe and Yvan Velenik
Ballistic Phase of Self-Interacting Random Walks (121K, latex2e) Oct 17, 07
Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

Abstract. We explain a unified approach to a study of ballistic phase for a large family of self-interacting random walks with a drift and self-interacting polymers with an external stretching force. The approach is based on a recent version of the Ornstein-Zernike theory developed in earlier works. It leads to local limit results for various observables (e.g. displacement of the end-point or number of hits of a fixed finite pattern) on paths of n-step walks (polymers) on all possible deviation scales from CLT to LD. The class of models, which display ballistic phase in the "universality class" discussed in the paper, includes self-avoiding walks, Domb-Joyce model, random walks in an annealed random potential, reinforced polymers and weakly reinforced random walks.

Files: 07-244.src( 07-244.keywords , IV07.tar.gz.mm )