Martin boundary of killed random walks on isoradial graphs

Cédric Boutillier; Kilian Raschel; Alin Bostan

Journal articles

Martin boundary of killed random walks on isoradial graphs

Cédric Boutillier ^{1, 2} Kilian Raschel ^{3, 4} Alin Bostan ⁵

1 LPSM (UMR_8001) - Laboratoire de Probabilités, Statistiques et Modélisations

2 IUF - Institut Universitaire de France

3 IDP - Institut Denis Poisson

4 CNRS - Centre National de la Recherche Scientifique

5 SPECFUN - Symbolic Special Functions : Fast and Certified

Inria Saclay - Ile de France

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.

Keywords : Killed random walk Isoradial graphs Martin boundary Green function Discrete exponential function

Document type :

Journal articles

Domain :

Mathematics [math] / Mathematical Physics [math-ph]

Mathematics [math] / Probability [math.PR]

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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 : Tuesday, January 11, 2022 - 5:56:35 PM

Martin boundary of killed random walks on isoradial graphs

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