Martin boundary of killed random walks on isoradial graphs

@article{Boutillier2019MartinBO,
  title={Martin boundary of killed random walks on isoradial graphs},
  author={C{\'e}dric Boutillier and K. Raschel},
  journal={arXiv: Probability},
  year={2019}
}
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. 

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