Pinning in non-critical half-space geometric last passage percolation
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| author | Das, Sayan Dimitrov, Evgeni Yang, Zongrui |
| author_facet | Das, Sayan Dimitrov, Evgeni Yang, Zongrui |
| contents | We study a symmetrized (half-space) version of geometric last passage percolation with a boundary parameter $c$ that interpolates between subcritical, critical, and supercritical behavior. This model gives rise to a family of interlacing random curves, or a line ensemble, which encode both the usual last passage time and its higher-rank analogues. Although these ensembles are understood in most space-time regions, their behavior near the diagonal -- where the boundary effects are strongest -- has remained unclear outside the critical regime. We determine the universal scaling limits of the line ensemble in this near-diagonal region for both subcritical ($c < 1$) and supercritical ($c > 1$) phases. In the subcritical case, after appropriate centering and scaling, the entire line ensemble converges to the pinned half-space Airy line ensemble, a universal Brownian Gibbsian object recently constructed as a canonical limit for half-space models in the KPZ universality class in arXiv:2601.04546. In the supercritical case, we prove an analogous convergence together with a curve-separation phenomenon: the lower curves converge to the same pinned half-space Airy limit, while the top curve decouples and converges to Brownian motion. These results essentially complete the asymptotic description of half-space geometric last passage percolation and provide a new rigorous instance of the pinned half-space Airy line ensemble as a universal scaling limit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_24616 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Pinning in non-critical half-space geometric last passage percolation Das, Sayan Dimitrov, Evgeni Yang, Zongrui Probability 82C22, 82B23 We study a symmetrized (half-space) version of geometric last passage percolation with a boundary parameter $c$ that interpolates between subcritical, critical, and supercritical behavior. This model gives rise to a family of interlacing random curves, or a line ensemble, which encode both the usual last passage time and its higher-rank analogues. Although these ensembles are understood in most space-time regions, their behavior near the diagonal -- where the boundary effects are strongest -- has remained unclear outside the critical regime. We determine the universal scaling limits of the line ensemble in this near-diagonal region for both subcritical ($c < 1$) and supercritical ($c > 1$) phases. In the subcritical case, after appropriate centering and scaling, the entire line ensemble converges to the pinned half-space Airy line ensemble, a universal Brownian Gibbsian object recently constructed as a canonical limit for half-space models in the KPZ universality class in arXiv:2601.04546. In the supercritical case, we prove an analogous convergence together with a curve-separation phenomenon: the lower curves converge to the same pinned half-space Airy limit, while the top curve decouples and converges to Brownian motion. These results essentially complete the asymptotic description of half-space geometric last passage percolation and provide a new rigorous instance of the pinned half-space Airy line ensemble as a universal scaling limit. |
| title | Pinning in non-critical half-space geometric last passage percolation |
| topic | Probability 82C22, 82B23 |
| url | https://arxiv.org/abs/2603.24616 |