The drift of a one-dimensional self-avoiding random walk. (English) Zbl 0792.60097

We prove that a self-avoiding random walk on the integers with bounded increments grows linearly. We characterize its drift in terms of the Frobenius eigenvalue of a certain one-parameter family of primitive matrices. As an important tool, we express the local times as a two-block functional of a certain Markov chain, which is of independent interest.
Reviewer: W.König (Zürich)


60K35 Interacting random processes; statistical mechanics type models; percolation theory
60G50 Sums of independent random variables; random walks
58E30 Variational principles in infinite-dimensional spaces
60F10 Large deviations
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