Self-trapping self-repelling random walks

TL;DR

This paper studies a modified self-avoiding walk model that transitions from self-repelling to self-trapping behavior, revealing subdiffusive, intermittent dynamics and high efficiency in covering finite lattices.

Contribution

It introduces a new self-repelling walk model exhibiting spontaneous transition to self-trapping, with detailed analysis of its dynamic regimes and cover time efficiency.

Findings

Walks become self-trapped after a characteristic time T*

In the trapped regime, walks are subdiffusive and intermittent

Walks efficiently cover finite lattices despite trapping

Abstract

Although the title seems self-contradictory, it does not contain a misprint. The model we study is a seemingly minor modification of the "true self-avoiding walk" (TSAW) model of Amit, Parisi, and Peliti in two dimensions. The walks in it are self-repelling up to a characteristic time $T^*$ (which depends on various parameters), but spontaneously (i.e., without changing any control parameter) become self-trapping after that. For free walks, $T^*$ is astronomically large, but on finite lattices the transition is easily observable. In the self-trapped regime, walks are subdiffusive and intermittent, spending longer and longer times in small areas until they escape and move rapidly to a new area. In spite of this, these walks are extremely efficient in covering finite lattices, as measured by average cover times.