A universality property for large deviations of RWRE close to the axis
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866915757488603136 |
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| author | Groisman, Pablo Ramírez, Alejandro F. Saglietti, Santiago Zaninovich, Sebastián |
| author_facet | Groisman, Pablo Ramírez, Alejandro F. Saglietti, Santiago Zaninovich, Sebastián |
| contents | We establish a general version of the strong KPZ universality conjecture near the axis for random walks in a random environment (RWRE) on $\mathbb{Z}^2$. For an i.i.d. elliptic random environment, we consider the quenched large deviations probabilities for trajectories starting at the origin and arriving at time $n+[n^a]$ to the position $(n,[n^a])$ and show that, if the logarithm of the right-jump probability has a finite moment of order $p>2$, then for $a < \frac{3}{7}(1-\frac{2}{p})$ the fluctuations of these propabilities are asymptotically governed by the GUE Tracy-Widom distribution. Our results are based on a comparison between RWRE and a last passage percolation model, whose asymptotic fluctuations near the axis were previously established independently by Bodineau-Martin and Baik-Suidan. Furthermore, we obtain also the full convergence to the directed landscape in this regime based on the extension of the aforementioned results to this setting by McKeown and Zhang. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_19024 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A universality property for large deviations of RWRE close to the axis Groisman, Pablo Ramírez, Alejandro F. Saglietti, Santiago Zaninovich, Sebastián Probability 60K35, 82C41 We establish a general version of the strong KPZ universality conjecture near the axis for random walks in a random environment (RWRE) on $\mathbb{Z}^2$. For an i.i.d. elliptic random environment, we consider the quenched large deviations probabilities for trajectories starting at the origin and arriving at time $n+[n^a]$ to the position $(n,[n^a])$ and show that, if the logarithm of the right-jump probability has a finite moment of order $p>2$, then for $a < \frac{3}{7}(1-\frac{2}{p})$ the fluctuations of these propabilities are asymptotically governed by the GUE Tracy-Widom distribution. Our results are based on a comparison between RWRE and a last passage percolation model, whose asymptotic fluctuations near the axis were previously established independently by Bodineau-Martin and Baik-Suidan. Furthermore, we obtain also the full convergence to the directed landscape in this regime based on the extension of the aforementioned results to this setting by McKeown and Zhang. |
| title | A universality property for large deviations of RWRE close to the axis |
| topic | Probability 60K35, 82C41 |
| url | https://arxiv.org/abs/2601.19024 |