On the convoy of the ASEP speed process
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912784998989824 |
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| author | Tian, Yuan |
| author_facet | Tian, Yuan |
| contents | We investigate the size of the convoy in the speed process in the multi-species asymmetric simple exclusion process (ASEP). Through a coupling argument, we obtain an exact formula for the expected convoy size by relating it to a combinatorial structure. We prove that the asymptotic expected convoy size is universal for all fixed jump rates $q \in [0,1)$. In the special case $q=0$, we upgrade this to full convergence in distribution. We further establish a critical scaling $q = 1 - γ/\sqrt{n}$ that yields a nontrivial limiting regime. Our analysis builds on Martin's construction of the convoy and makes use of an orthogonal-polynomial representation of random-walk transition probabilities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_19897 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the convoy of the ASEP speed process Tian, Yuan Probability Mathematical Physics Combinatorics We investigate the size of the convoy in the speed process in the multi-species asymmetric simple exclusion process (ASEP). Through a coupling argument, we obtain an exact formula for the expected convoy size by relating it to a combinatorial structure. We prove that the asymptotic expected convoy size is universal for all fixed jump rates $q \in [0,1)$. In the special case $q=0$, we upgrade this to full convergence in distribution. We further establish a critical scaling $q = 1 - γ/\sqrt{n}$ that yields a nontrivial limiting regime. Our analysis builds on Martin's construction of the convoy and makes use of an orthogonal-polynomial representation of random-walk transition probabilities. |
| title | On the convoy of the ASEP speed process |
| topic | Probability Mathematical Physics Combinatorics |
| url | https://arxiv.org/abs/2512.19897 |