Multispecies inhomogeneous $t$-PushTASEP with general capacity
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908840629370880 |
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| author | Ayyer, Arvind Kuniba, Atsuo |
| author_facet | Ayyer, Arvind Kuniba, Atsuo |
| contents | We study an $n$-species $t$-PushTASEP, an integrable long-range stochastic process, on a one-dimensional periodic lattice with inhomogeneities $x_1,\ldots,x_L$ and arbitrary capacity $l$ at each lattice site. The Markov matrix is identified with an alternating sum of commuting transfer matrices over all fundamental representations of $U_t(\widehat{sl}_{n+1})$. Stationary probabilities are expressed in a matrix product form involving a fusion of quantized corner transfer matrices for the strange five-vertex model introduced by Okado, Scrimshaw, and the second author. The resulting partition function, which serves as the normalization factor of the stationary probabilities, is obtained from the $l=1$ case by a finite plethystic substitution of length $l$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_17179 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Multispecies inhomogeneous $t$-PushTASEP with general capacity Ayyer, Arvind Kuniba, Atsuo Mathematical Physics Combinatorics Probability Quantum Algebra Primary:60J27, Secondary: 82B23, 81R50, 82B20 We study an $n$-species $t$-PushTASEP, an integrable long-range stochastic process, on a one-dimensional periodic lattice with inhomogeneities $x_1,\ldots,x_L$ and arbitrary capacity $l$ at each lattice site. The Markov matrix is identified with an alternating sum of commuting transfer matrices over all fundamental representations of $U_t(\widehat{sl}_{n+1})$. Stationary probabilities are expressed in a matrix product form involving a fusion of quantized corner transfer matrices for the strange five-vertex model introduced by Okado, Scrimshaw, and the second author. The resulting partition function, which serves as the normalization factor of the stationary probabilities, is obtained from the $l=1$ case by a finite plethystic substitution of length $l$. |
| title | Multispecies inhomogeneous $t$-PushTASEP with general capacity |
| topic | Mathematical Physics Combinatorics Probability Quantum Algebra Primary:60J27, Secondary: 82B23, 81R50, 82B20 |
| url | https://arxiv.org/abs/2602.17179 |