Optimal-order exit point bounds in exponential last-passage percolation via the coupling technique
Optimal-order exit point bounds in exponential last-passage percolation via the coupling technique
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DOI：
10.2140/pmp.2023.4.609
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发表时间：
2021-05
期刊：
影响因子：
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通讯作者：
Elnur Emrah;Christopher Janjigian;T. Seppalainen
中科院分区：
文献类型：
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作者：
Elnur Emrah;Christopher Janjigian;T. Seppalainen
我们开发了一种新的概率方法，用于导出定向平面聚合物和渗流模型中的偏差估计。关键的估计是出口点的测地线，因为他们通过横向右下边界。这些界限是最佳的指数级。我们推导出他们的背景下，最后一次通过渗滤指数权重与近稳态边界条件。其结果是，概率耦合方法被授权处理各种问题的最佳化，这可以实现以前只能通过输入可积概率。作为在批量设置中的应用，我们得到了测地线的横向波动的指数阶的上界，以及分布Busemann极限和竞争界面极限的对数修正的立方根上界。其他几个应用程序已经在文献中。
We develop a new probabilistic method for deriving deviation estimates in directed planar polymer and percolation models. The key estimates are for exit points of geodesics as they cross transversal down-right boundaries. These bounds are of optimal cubic-exponential order. We derive them in the context of last-passage percolation with exponential weights with near-stationary boundary conditions. As a result, the probabilistic coupling method is empowered to treat a variety of problems optimally, which could previously be achieved only via inputs from integrable probability. As applications in the bulk setting, we obtain upper bounds of cubic-exponential order for transversal fluctuations of geodesics, and cube-root upper bounds with a logarithmic correction for distributional Busemann limits and competition interface limits. Several other applications are already in the literature.