The directed landscape in half-space
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866909024911360000 |
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| author | Dauvergne, Duncan Zhang, Lingfu |
| author_facet | Dauvergne, Duncan Zhang, Lingfu |
| contents | We prove that two half-space models in the KPZ universality class, exponential last-passage percolation and a family of Poisson-avoiding metrics generalizing colored TASEP, converge to a common scaling limit. This scaling limit is the directed landscape in half-space, a random directed metric in the half-plane indexed by a parameter which determines the strength of the boundary interaction.
As part of our analysis, we characterize the half-space directed landscape in terms of the half-space KPZ fixed point, and prove convergence of geodesics. We also give an explicit construction of joint stationary measures (or horizons) in half-space for the log-gamma polymer, the KPZ equation, exponential and geometric last passage percolation, and the directed landscape itself. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_10020 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The directed landscape in half-space Dauvergne, Duncan Zhang, Lingfu Probability Mathematical Physics We prove that two half-space models in the KPZ universality class, exponential last-passage percolation and a family of Poisson-avoiding metrics generalizing colored TASEP, converge to a common scaling limit. This scaling limit is the directed landscape in half-space, a random directed metric in the half-plane indexed by a parameter which determines the strength of the boundary interaction. As part of our analysis, we characterize the half-space directed landscape in terms of the half-space KPZ fixed point, and prove convergence of geodesics. We also give an explicit construction of joint stationary measures (or horizons) in half-space for the log-gamma polymer, the KPZ equation, exponential and geometric last passage percolation, and the directed landscape itself. |
| title | The directed landscape in half-space |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2604.10020 |