One-point large deviations of the directed landscape geodesic
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913733075271680 |
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| author | Spivak, Daniel |
| author_facet | Spivak, Daniel |
| contents | The directed landscape, the central object in the Kardar-Parisi-Zhang universality class, is shown to be the scaling limit of various models by Dauvergne and Virág (2022) and Dauvergne, Ortmann and Virág (2018). In his study of geodesics in upper tail deviations of the directed landscape, Liu (2022) put forward a conjecture about the rate of the lowest rate metric under which a geodesic between two points passes through a particular point between them. Das, Dauvergne and Virág (2024) disproved his conjecture, and made a conjecture of their own. This paper disproves that conjecture and puts the question to rest with an answer and a proof. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_09486 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | One-point large deviations of the directed landscape geodesic Spivak, Daniel Probability Mathematical Physics The directed landscape, the central object in the Kardar-Parisi-Zhang universality class, is shown to be the scaling limit of various models by Dauvergne and Virág (2022) and Dauvergne, Ortmann and Virág (2018). In his study of geodesics in upper tail deviations of the directed landscape, Liu (2022) put forward a conjecture about the rate of the lowest rate metric under which a geodesic between two points passes through a particular point between them. Das, Dauvergne and Virág (2024) disproved his conjecture, and made a conjecture of their own. This paper disproves that conjecture and puts the question to rest with an answer and a proof. |
| title | One-point large deviations of the directed landscape geodesic |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2503.09486 |