AI 中文总结
本文通过 Peierls 论证和转移矩阵方法，证明平面软棒渗流的临界参数 $\epsilon_c \le 0.99$，并在该参数下建立正向渗流。
AI 中文摘要
在平面软棒渗流中，方格晶格的每个顶点独立地打开一个均匀选择的出射箭头，并以概率 $\epsilon$ 同时打开相反方向的箭头。受 Bäumler 等人提出的关于其临界参数问题的启发，我们证明 $\epsilon_{c}\le0.99<1$，从而在双箭头端点之下建立渗流。更精确地，在 $\epsilon=0.99$ 时，原点具有无限向前簇的概率大于 11/20。证明使用了 Peierls 论证，其中边界转向由三态转移矩阵编码以界定轮廓和。
英文摘要
In planar soft-stick percolation, each vertex of the square lattice independently opens one uniformly chosen outgoing arrow and, with probability $ε$, the opposite arrow as well. Motivated by the question on its critical parameter raised by Bäumler et al., we prove that $ε_{c}\le0.99<1$, establishing percolation below the two-arrow endpoint. More precisely, at $ε=0.99$ the origin has an infinite forward cluster with probability greater than 11/20. The proof uses a Peierls argument in which boundary turns are encoded by a three-state transfer matrix to bound the contour sum.
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