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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.08341 |
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| _version_ | 1866912269936361472 |
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| author | Tian, Yuan |
| author_facet | Tian, Yuan |
| contents | In this paper we study the oriented swap process on the positive integers and its asymptotic properties. Our results extend a theorem by Angel, Holroyd, and Romik regarding the trajectories of particles in the finite oriented swap process. Furthermore, we study the evolution of the type of a particle at the leftmost position over time. Our approach relies on a relationship between multi-species particle systems and Hecke algebras, complemented by a detailed asymptotic analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_08341 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The oriented swap process on half line Tian, Yuan Probability Mathematical Physics In this paper we study the oriented swap process on the positive integers and its asymptotic properties. Our results extend a theorem by Angel, Holroyd, and Romik regarding the trajectories of particles in the finite oriented swap process. Furthermore, we study the evolution of the type of a particle at the leftmost position over time. Our approach relies on a relationship between multi-species particle systems and Hecke algebras, complemented by a detailed asymptotic analysis. |
| title | The oriented swap process on half line |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2503.08341 |