Stuck Walks
Anna Erschler, Balint Toth, Wendelin Werner

TL;DR
This paper studies a class of self-interacting random walks on the integer line, showing that under certain conditions they become confined to finite intervals due to the interplay of attraction and repulsion effects.
Contribution
It provides a rigorous analysis of the asymptotic behavior of self-interacting walks, identifying conditions for confinement based on model parameters.
Findings
Random walks can be confined to finite intervals depending on parameters.
Self-attracting effects dominate in certain parameter regimes.
The model demonstrates the balance between attraction and repulsion influences.
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsStochastic processes and statistical mechanics · Theoretical and Computational Physics · Quasicrystal Structures and Properties
