Multispecies inhomogeneous $t$-PushTASEP from antisymmetric fusion
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911326933090304 |
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| author | Ayyer, Arvind Kuniba, Atsuo |
| author_facet | Ayyer, Arvind Kuniba, Atsuo |
| contents | We investigate the recently introduced inhomogeneous $n$-species $t$-PushTASEP, a long-range stochastic process on a periodic lattice. A Baxter-type formula is established, expressing the Markov matrix as an alternating sum of commuting transfer matrices over all the fundamental representations of $U_t(\widehat{sl}_{n+1})$. This superposition acts as an inclusion-exclusion principle, selectively extracting the sequential particle transitions characteristic of the PushTASEP, while canceling forbidden channels. The homogeneous specialization connects the PushTASEP to ASEP, showing that the two models share eigenstates and a common integrability structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_00829 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multispecies inhomogeneous $t$-PushTASEP from antisymmetric fusion Ayyer, Arvind Kuniba, Atsuo Mathematical Physics Combinatorics Probability Quantum Algebra 60J27, 82B20, 82B23, 82B44, 81R50, 17B37 We investigate the recently introduced inhomogeneous $n$-species $t$-PushTASEP, a long-range stochastic process on a periodic lattice. A Baxter-type formula is established, expressing the Markov matrix as an alternating sum of commuting transfer matrices over all the fundamental representations of $U_t(\widehat{sl}_{n+1})$. This superposition acts as an inclusion-exclusion principle, selectively extracting the sequential particle transitions characteristic of the PushTASEP, while canceling forbidden channels. The homogeneous specialization connects the PushTASEP to ASEP, showing that the two models share eigenstates and a common integrability structure. |
| title | Multispecies inhomogeneous $t$-PushTASEP from antisymmetric fusion |
| topic | Mathematical Physics Combinatorics Probability Quantum Algebra 60J27, 82B20, 82B23, 82B44, 81R50, 17B37 |
| url | https://arxiv.org/abs/2503.00829 |