2025/06/02 by Włodek Bryc, Bryc, Wlodek, Kamil Szpojankowski +3
Mathematics · Physics and Astronomy · #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2506.01879
openalex publication_date 2025/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Barraquand, Corwin, and Yang arXiv:2306.05983 established that geometric last passage percolation (LPP) on a strip of ℤ2 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.