We consider killed planar random walks on isoradial graphs. Contrary to the lattice case, isoradial graphs are not translation invariant, do not admit any group structure and are spatially non-homogeneous. Despite these crucial differences, we compute the asymptotics of the Martin kernel, deduce the Martin boundary and show that it is minimal. Similar results on the grid \(\mathbb {Z}^{d}\) are derived in a celebrated work of Ney and Spitzer.

中文翻译：

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等角线图上被杀死的随机游走的马丁边界

我们考虑在等径图上杀死了平面随机游走。与晶格情况相反，等辐射线图不是平移不变的，不容许任何组结构并且在空间上是不均匀的。尽管存在这些关键差异，但我们计算了马丁核的渐近性，推导了马丁边界，并证明了该边界是最小的。Ney和Spitzer的一项著名著作得出了在网格\（\ mathbb {Z} ^ {d} \）上的类似结果。