Classification of the eternal solutions and multiple coalescing shocks in the KPZ fixed point
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866911716754849792 |
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| author | Bhattacharjee, Sudeshna Busani, Ofer Sorensen, Evan |
| author_facet | Bhattacharjee, Sudeshna Busani, Ofer Sorensen, Evan |
| contents | We give a complete classification of the eternal solutions for the KPZ fixed point. Each of these is a (possibly infinite) patching together of the known eternal solutions, called Busemann functions. The resulting evolution of the KPZ fixed point exhibits a shock at each of the boundaries between the different Busemann functions. Moving forward in time, the shocks coalesce, while moving backwards in time, additional shocks can form. We describe several geometric properties of this tree of shocks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_26048 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Classification of the eternal solutions and multiple coalescing shocks in the KPZ fixed point Bhattacharjee, Sudeshna Busani, Ofer Sorensen, Evan Probability Mathematical Physics 60K35 We give a complete classification of the eternal solutions for the KPZ fixed point. Each of these is a (possibly infinite) patching together of the known eternal solutions, called Busemann functions. The resulting evolution of the KPZ fixed point exhibits a shock at each of the boundaries between the different Busemann functions. Moving forward in time, the shocks coalesce, while moving backwards in time, additional shocks can form. We describe several geometric properties of this tree of shocks. |
| title | Classification of the eternal solutions and multiple coalescing shocks in the KPZ fixed point |
| topic | Probability Mathematical Physics 60K35 |
| url | https://arxiv.org/abs/2605.26048 |