Raschel, Kilian Green functions and Martin compactification for killed random walks related to \(SU(3)\). (English) Zbl 1226.60068 Electron. Commun. Probab. 15, 176-190 (2010). Summary: We consider 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 asymptotics of the Green functions along all infinite paths of states, and from this, we deduce that the Martin compactification is the one-point compactification. Cited in 7 Documents MSC: 60G50 Sums of independent random variables; random walks 31C35 Martin boundary theory 30F10 Compact Riemann surfaces and uniformization Keywords:killed random walks; Green functions; Martin compactification; uniformization PDFBibTeX XMLCite \textit{K. Raschel}, Electron. Commun. Probab. 15, 176--190 (2010; Zbl 1226.60068) Full Text: DOI arXiv EMIS