Stuck Walks

Anna Erschler; Balint Toth; Wendelin Werner

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arXiv · 1011.1103

Stuck Walks

Anna Erschler·Balint Toth·Wendelin Werner

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Abstract

We investigate the asymptotic behaviour of a class of self-interacting nearest neighbour random walks on the one-dimensional integer lattice which are pushed by a particular linear combination of their own local time on edges in the neighbourhood of their current position. We prove that in a range of the relevant parameter of the model such random walkers can be eventually confined to a finite interval of length depending on the parameter value. The phenomenon arises as a result of competing self-attracting and self-repelling effects where in the named parameter range the former wins.

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Anna Erschler, Balint Toth, Wendelin Werner. 2010-11-04. Stuck Walks. https://arxiv.org/abs/1011.1103

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