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2010 Green functions and Martin compactification for killed random walks related to SU(3)
Kilian Raschel
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Electron. Commun. Probab. 15: 176-190 (2010). DOI: 10.1214/ECP.v15-1543

Abstract

We consider the random walks killed at the boundary of the quarter plane, with homogeneous non-zero jump probabilities to the eight nearest neighbors and drift zero in the interior, and which admit a positive harmonic polynomial of degree three. For these processes, we find the asymptotic of the Green functions along all infinite paths of states, and from this we deduce that the Martin compactification is the one-point compactification.

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Kilian Raschel. "Green functions and Martin compactification for killed random walks related to SU(3)." Electron. Commun. Probab. 15 176 - 190, 2010. https://doi.org/10.1214/ECP.v15-1543

Information

Accepted: 27 May 2010; Published: 2010
First available in Project Euclid: 6 June 2016

zbMATH: 1226.60068
MathSciNet: MR2651549
Digital Object Identifier: 10.1214/ECP.v15-1543

Subjects:
Primary: 31C35, 60G50
Secondary: 30F10

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