Universal Fluctuations in the Tail Probability for d=2 Random Walks in Space-Time Random Environments
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915456676265984 |
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| author | Ark, Franscesca Hass, Jacob B. Corwin, Eric I. |
| author_facet | Ark, Franscesca Hass, Jacob B. Corwin, Eric I. |
| contents | Many diffusive systems involve correlated random walkers due to a shared environment. Such systems can be modeled as random walks in random environments (RWRE). These models differ from classical diffusion in the behavior of the extremes -- the walkers that move the fastest or farthest. In spatial dimension $d=1$ RWRE models have been well studied numerically and analytically and exhibit universal behavior in the Kardar-Parisi-Zhang universality class. Here, we study discrete lattice RWRE models in $d=2$. We find that the tail probability exhibits a different universal scaling form, which is nevertheless characterized by the same coefficient, $λ_\mathrm{ext}$, as in the $d=1$ case. We observe a critical scaling regime for fluctuations in the tail probability at positions that scale linearly in time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_15999 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Universal Fluctuations in the Tail Probability for d=2 Random Walks in Space-Time Random Environments Ark, Franscesca Hass, Jacob B. Corwin, Eric I. Statistical Mechanics Many diffusive systems involve correlated random walkers due to a shared environment. Such systems can be modeled as random walks in random environments (RWRE). These models differ from classical diffusion in the behavior of the extremes -- the walkers that move the fastest or farthest. In spatial dimension $d=1$ RWRE models have been well studied numerically and analytically and exhibit universal behavior in the Kardar-Parisi-Zhang universality class. Here, we study discrete lattice RWRE models in $d=2$. We find that the tail probability exhibits a different universal scaling form, which is nevertheless characterized by the same coefficient, $λ_\mathrm{ext}$, as in the $d=1$ case. We observe a critical scaling regime for fluctuations in the tail probability at positions that scale linearly in time. |
| title | Universal Fluctuations in the Tail Probability for d=2 Random Walks in Space-Time Random Environments |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2508.15999 |