# 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