Invariant measures of exclusion processes with a look-ahead rule
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866911562813407232 |
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| author | Nhung, Lam Thi Ngoc, Ngo Phuoc Nguyen Thi, Huynh Anh |
| author_facet | Nhung, Lam Thi Ngoc, Ngo Phuoc Nguyen Thi, Huynh Anh |
| contents | We study a one-dimensional exclusion process with a fixed jump length $I \ge 1$ in which a particle may advance or retreat $I$ sites provided all intermediate sites are vacant, with hopping rates of Arrhenius type depending on the local headway. We identify the class of rates admitting an explicit Ising-Gibbs invariant measure, with stationarity governed by pairwise balance rather than detailed balance. In the thermodynamic limit, we derive a closed-form stationary current that recovers the mean-field prediction for look-ahead traffic flow models exactly when particles are uncorrelated, and quantifies the correlation-induced correction for non-trivial interactions, illustrated with two explicit families of interaction potentials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_01796 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Invariant measures of exclusion processes with a look-ahead rule Nhung, Lam Thi Ngoc, Ngo Phuoc Nguyen Thi, Huynh Anh Statistical Mechanics We study a one-dimensional exclusion process with a fixed jump length $I \ge 1$ in which a particle may advance or retreat $I$ sites provided all intermediate sites are vacant, with hopping rates of Arrhenius type depending on the local headway. We identify the class of rates admitting an explicit Ising-Gibbs invariant measure, with stationarity governed by pairwise balance rather than detailed balance. In the thermodynamic limit, we derive a closed-form stationary current that recovers the mean-field prediction for look-ahead traffic flow models exactly when particles are uncorrelated, and quantifies the correlation-induced correction for non-trivial interactions, illustrated with two explicit families of interaction potentials. |
| title | Invariant measures of exclusion processes with a look-ahead rule |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2604.01796 |