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Green functions and Martin compactification for killed random walks related to \(SU(3)\). (English) Zbl 1226.60068

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.

MSC:

60G50 Sums of independent random variables; random walks
31C35 Martin boundary theory
30F10 Compact Riemann surfaces and uniformization
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