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Martin boundary of killed random walks on isoradial graphs

Abstract : 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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Contributor : Kilian Raschel <>
Submitted on : Sunday, December 22, 2019 - 11:18:23 AM
Last modification on : Monday, December 14, 2020 - 5:38:14 PM
Long-term archiving on: : Monday, March 23, 2020 - 1:13:54 PM


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  • HAL Id : hal-02422417, version 1


Cédric Boutillier, Kilian Raschel, Alin Bostan. Martin boundary of killed random walks on isoradial graphs. 2019. ⟨hal-02422417⟩



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