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.Comment: 13 page
