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

Kilian Raschel (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

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.

Mots clés: Random walk; Green functions; Martin boundary; Absorption probabilities; Random walk

Domaines: Probabilités [math.PR]

Kilian Raschel. Green functions and Martin compactification for killed random walks related to SU(3). Electronic Communications in Probability, 2010, 15 (17), pp.176-190. ⟨hal-00425651v2⟩