Green functions and Martin compactification for killed random walks related to SU(3)

Kilian Raschel (Universite Pierre et Marie Curie)

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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Pages: 176-190

Publication Date: May 27, 2010

DOI: 10.1214/ECP.v15-1543

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