Self-trapping self-repelling random walks

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 $T^{\ast }$ (which depends on various parameters), but spontaneously (i.e., without changing any control parameter) become self-trapping after that. For free walks, $T^{\ast }$ 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.

5 pages main paper + 5 pages supplementary material

References in corpus (2)

• Intermittent search strategies
• How fast does a random walk cover a torus?

Cited by in corpus (10)

• Chemotactic self-caging in active emulsions
• Optimal non-Markovian search strategies with n-step memory
• Joint statistics of space and time exploration of $1d$ random walks
• Large Deviations of Convex Hulls of the "True" Self-Avoiding Random Walk
• Range-controlled random walks
• Stochastic Resetting Mitigates Latent Gradient Bias of SGD from Label Noise
• Universal Negative Energetic Elasticity in Polymer Chains: Crossovers among Random, Self-Avoiding, and Neighbor-Avoiding Walks
• Self-Repelling Bi-Exploration Process
• Anomalous Diffusion and Emergent Universality in Coupled Memory-Driven Systems
• Self-interacting processes via Doob conditioning