Ballistic phase of self-interacting random walks.

*(English)*Zbl 1255.60168
MĂ¶rters, Peter (ed.) et al., Analysis and stochastics of growth processes and interface models. Selected papers based on the presentations at a regional meeting of the London Mathematical Society and a workshop on ‘Analysis and stochastics of growth processes’, Bath, UK, September 11–15, 2006. Oxford: Oxford University Press (ISBN 978-0-19-923925-2/hbk). 55-79 (2008).

Summary: 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.

For the entire collection see [Zbl 1144.60003].

For the entire collection see [Zbl 1144.60003].

##### MSC:

60K35 | Interacting random processes; statistical mechanics type models; percolation theory |

82B31 | Stochastic methods applied to problems in equilibrium statistical mechanics |

82B41 | Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics |

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\textit{D. Ioffe} and \textit{Y. Velenik}, in: Analysis and stochastics of growth processes and interface models. Selected papers based on the presentations at a regional meeting of the London Mathematical Society and a workshop on `Analysis and stochastics of growth processes', Bath, UK, September 11--15, 2006. Oxford: Oxford University Press. 55--79 (2008; Zbl 1255.60168)

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