标题： 自由Askey--Wilson泛函与条状几何last passage渗流 显示英文标题

标题： Free Askey--Wilson functionals and geometric last passage percolation on a strip

摘要： 巴拉坎、科文和杨在arXiv:2306.05983中证明了在宽度为$\mathbb{Z}^2$的条带上的几何型最后通过渗流（LPP）具有唯一的平稳测度。 在此基础上，巴拉坎在arXiv:2409.08927中推导出了该模型多点概率生成函数的显式围道积分公式。 本文中，我们引入自由Askey--Wilson泛函，并利用它们扩展这些生成函数公式。 我们的框架给出了比之前可及范围更广的边界参数的显式表达式。 这一推广使我们能够确定刻画平稳测度的大尺度渐近性如何依赖于边界条件的完整相图。 此外，当参数随条带宽度变化时，我们还证明了平稳测度的泊松逼近。 显示英文摘要

摘要： 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.