Abstract

Ballistic Phase of Self-Interacting Random Walks D. Ioffe, Y. Velenik In "Analysis and Stochastics of Growth Processes and Interface Models", P. Mörters et al. (eds), Oxford University Press , 55-79 (2008). 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. 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. Key words: Ornstein-Zernike theory, self-interacting random walks and polymers, ballistic phase, local limit theorem, functional CLT, reinforced random walk, SAW, Domb-Joyce model, random walk in annealed random environment Files: PDF file, bibtex