Work

Sokoban random walk: From environment reshaping to trapping crossover

Year: 2026

Type: article

Abstract: We study the dynamics of a moving in a disordered medium with obstacle density ρ . In contrast to the classic model of de Gennes with static obstacles that exhibits a percolation transition, the Sokoban walker is capable of modifying its environment by pushing a few surrounding obstacles. Surprisingly, even a limited pushing ability leads to a loss of the percolation transition. Through a combination of a rigorous large-deviation calculation and extensive numerical simulations, we demonstrate that the Sokoban model belongs to the Balagurov-Vaks-Donsker-Varadhan trapping universality class. The survival probability that the walker has not yet been trapped inside a cage exhibits stretched-exponential relaxation at late times. Furthermore, using the average trap size as a proxy, we identify the emergence of a dynamical crossover at a density ρ * ≈ 0.55 between two qualitatively different trapping mechanisms: a self-trapping mechanism at low density, where the walker becomes dynamically localized within a self-formed trap, and a pre-existing trapping mechanism at high density, where confinement arises from the initial arrangement of obstacles. This crossover is responsible for the loss of the classical percolation transition.

Source: Physical Review Research

DOI: 10.1103/qqws-k8pw

Authors: Prashant Singh, David A. Kessler, Eli Barkai

Institution: Bar-Ilan University

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,625

Funder: Israel Science Foundation