Stuck walks

Anna Erschler, Balint A Toth, Wendelin Werner

Research output: Contribution to journalArticle (Academic Journal)peer-review

5 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)149-163
Number of pages15
JournalProbability Theory and Related Fields
Issue number1-2
Publication statusPublished - Oct 2012


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