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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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https://hal.archives-ouvertes.fr/hal-02422417
Contributor : Kilian Raschel Connect in order to contact the contributor
Submitted on : Friday, February 5, 2021 - 10:16:30 AM
Last modification on : Friday, January 21, 2022 - 3:19:53 AM

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Boutillier-Raschel-21.pdf
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  • HAL Id : hal-02422417, version 2

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Cédric Boutillier, Kilian Raschel, Alin Bostan. Martin boundary of killed random walks on isoradial graphs. Potential Analysis, Springer Verlag, In press. ⟨hal-02422417v2⟩

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