Free Askey--Wilson functionals and geometric last passage percolation on a strip
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912409601441792 |
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| author | Bryc, Wlodek Szpojankowski, Kamil Wesolowski, Jacek |
| author_facet | Bryc, Wlodek Szpojankowski, Kamil Wesolowski, Jacek |
| contents | Barraquand, Corwin, and Yang arXiv:2306.05983 established that geometric last passage percolation (LPP) on a strip of $\mathbb{Z}^2$ has a unique stationary measure. Building on this, Barraquand arXiv:2409.08927 derived explicit contour integral formulas for the model's multipoint probability generating function. In this paper, we introduce free Askey--Wilson functionals and use them to extend these generating function formulas. Our framework yields explicit expressions valid over a broader range of boundary parameters than previously accessible. This generalization allows us to determine the full phase diagram that characterizes how the large-scale asymptotics of the stationary measure depend on the boundary conditions. In addition, we prove a Poisson approximation for the stationary measure when the parameters vary with the strip width. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_01879 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Free Askey--Wilson functionals and geometric last passage percolation on a strip Bryc, Wlodek Szpojankowski, Kamil Wesolowski, Jacek Probability Barraquand, Corwin, and Yang arXiv:2306.05983 established that geometric last passage percolation (LPP) on a strip of $\mathbb{Z}^2$ has a unique stationary measure. Building on this, Barraquand arXiv:2409.08927 derived explicit contour integral formulas for the model's multipoint probability generating function. In this paper, we introduce free Askey--Wilson functionals and use them to extend these generating function formulas. Our framework yields explicit expressions valid over a broader range of boundary parameters than previously accessible. This generalization allows us to determine the full phase diagram that characterizes how the large-scale asymptotics of the stationary measure depend on the boundary conditions. In addition, we prove a Poisson approximation for the stationary measure when the parameters vary with the strip width. |
| title | Free Askey--Wilson functionals and geometric last passage percolation on a strip |
| topic | Probability |
| url | https://arxiv.org/abs/2506.01879 |