The directed landscape
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2018
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| _version_ | 1866909178466926592 |
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| author | Dauvergne, Duncan Ortmann, Janosch Virag, Balint |
| author_facet | Dauvergne, Duncan Ortmann, Janosch Virag, Balint |
| contents | The conjectured limit of last passage percolation is a scale-invariant, independent, stationary increment process with respect to metric composition. We prove this for Brownian last passage percolation. We construct the Airy sheet and characterize it in terms of the Airy line ensemble. We also show that last passage geodesics converge to random functions with Holder-2/3- continuous paths. This work completes the construction of the central object in the Kardar-Parisi-Zhang universality class, the directed landscape. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1812_00309 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | The directed landscape Dauvergne, Duncan Ortmann, Janosch Virag, Balint Probability Mathematical Physics 60K35, 60B20 The conjectured limit of last passage percolation is a scale-invariant, independent, stationary increment process with respect to metric composition. We prove this for Brownian last passage percolation. We construct the Airy sheet and characterize it in terms of the Airy line ensemble. We also show that last passage geodesics converge to random functions with Holder-2/3- continuous paths. This work completes the construction of the central object in the Kardar-Parisi-Zhang universality class, the directed landscape. |
| title | The directed landscape |
| topic | Probability Mathematical Physics 60K35, 60B20 |
| url | https://arxiv.org/abs/1812.00309 |