两层舒尔和惠特克过程的积分公式

Guillaume Barraquand
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引用次数: 0

摘要

arXiv:2306.05983使用舒尔和维特克过程的变体(称为两层吉布斯量)描述了在$\mathbb Z^2$晶格的条带中具有几何权重和对数伽马聚合物的最后通道渗流的静态量。在本文中,我们证明了描述两层舒尔和惠特克过程的多点联合分布的等高线积分公式。我们还将它们表示为具有明确过渡核的 Doob 变换马尔可夫过程。作为公式应用的一个例子,我们计算了具有任意边界参数的 $[0,L]$ 上 KPZ 方程的增长率。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Integral formulas for two-layer Schur and Whittaker processes
Stationary measures of last passage percolation with geometric weights and the log-gamma polymer in a strip of the $\mathbb Z^2$ lattice are characterized in arXiv:2306.05983 using variants of Schur and Whittaker processes, called two-layer Gibbs measures. In this article, we prove contour integral formulas characterizing the multipoint joint distribution of two-layer Schur and Whittaker processes. We also express them as Doob transformed Markov processes with explicit transition kernels. As an example of application of our formulas, we compute the growth rate of the KPZ equation on $[0,L]$ with arbitrary boundary parameters.
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