This paper gives a self-contained proof of the non-existence of nontrivial bi-infinite geodesics in directed planar last-passage percolation with exponential weights. The techniques used are couplings, coarse graining, and control of geodesics through planarity and estimates derived from increment-stationary versions of the last-passage percolation process.

中文翻译：

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指数角增长模型中不存在双无限测地线

本文给出了一个独立的证明，证明在具有指数权重的定向平面最后通道渗透中不存在非平凡双无限测地线。使用的技术是耦合、粗粒度和通过平面度控制测地线，以及从最后通道渗透过程的增量固定版本得出的估计。