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  • Letter
  • Open Access

Sokoban random walk: From environment reshaping to trapping crossover

Prashant Singh1,*, David A. Kessler1, and Eli Barkai1,2

  • *Contact author: prashantsinghramitay@gmail.com
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Phys. Rev. Research 8, L012023 – Published 26 January, 2026

DOI: https://doi.org/10.1103/qqws-k8pw

Abstract

We study the dynamics of a Sokoban random walker 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.

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Phys. Rev. Research 8, L012023– Published 26 January, 2026
  • Received 24 August 2025
  • Accepted 6 January 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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