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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2602.14180 |
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| _version_ | 1866917285502910464 |
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| author | Singh, Prashant Barkai, Eli Kessler, David A |
| author_facet | Singh, Prashant Barkai, Eli Kessler, David A |
| contents | We study caging/trapping in Sokoban-type models, featuring a random walker moving through a disordered medium of obstacles and capable of pushing some obstacles blocking its path. In one-dimension, we allow the walker to push up to an arbitrary $N_{\rm P}$ number of obstacles. For $N_{\rm P}\gg 1$, we use large-deviation theory to show that the survival probability to remain uncaged exhibits crossover from an exponential decay with time at intermediate times to a stretched-exponential decay at long times, with an exponent $1/3$ independent of $N_{\rm P}$. The long-time exponent matches the Balagurov--Vaks--Donsker--Varadhan (BVDV) theory of the classical trapping problem, while the exponential decay is qualitatively distinct from the Rosenstock's intermediate-time theory for classical trapping. Similarly, in two dimensions, numerical simulations reveal that both the Sokoban model and its generalized version exhibit long-time stretched-exponential relaxation with exponent $1/2$, again consistent with the BVDV theory. Finally, in two dimensions, we find that the mean trap size is nonmonotonic in $ρ$: it is small at both low and high densities, but reaches a peak at a characteristic density $ρ_*$. We estimate $ρ_* \approx 0.55$ for the Sokoban model and $ρ_* \approx 0.675$ for the generalized Sokoban model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_14180 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Sokoban Random Walk: A Trapping Perspective Singh, Prashant Barkai, Eli Kessler, David A Statistical Mechanics We study caging/trapping in Sokoban-type models, featuring a random walker moving through a disordered medium of obstacles and capable of pushing some obstacles blocking its path. In one-dimension, we allow the walker to push up to an arbitrary $N_{\rm P}$ number of obstacles. For $N_{\rm P}\gg 1$, we use large-deviation theory to show that the survival probability to remain uncaged exhibits crossover from an exponential decay with time at intermediate times to a stretched-exponential decay at long times, with an exponent $1/3$ independent of $N_{\rm P}$. The long-time exponent matches the Balagurov--Vaks--Donsker--Varadhan (BVDV) theory of the classical trapping problem, while the exponential decay is qualitatively distinct from the Rosenstock's intermediate-time theory for classical trapping. Similarly, in two dimensions, numerical simulations reveal that both the Sokoban model and its generalized version exhibit long-time stretched-exponential relaxation with exponent $1/2$, again consistent with the BVDV theory. Finally, in two dimensions, we find that the mean trap size is nonmonotonic in $ρ$: it is small at both low and high densities, but reaches a peak at a characteristic density $ρ_*$. We estimate $ρ_* \approx 0.55$ for the Sokoban model and $ρ_* \approx 0.675$ for the generalized Sokoban model. |
| title | The Sokoban Random Walk: A Trapping Perspective |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2602.14180 |