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We consider a family of random walks killed at the boundary of the Weylchamber of the dual of $\rm{Sp}(4)$, which in addition satisfies the followingproperty: for any $n\geq 3$, there is in this family a walk associated with areflection group of order $2n$. Moreover, the case $n=4$ corresponds to aprocess which appears naturally by studying quantum random walks on the dual of$\rm{Sp}(4)$. For all the processes belonging to this family, we find the exactasymptotic of the Green functions along all infinite paths of states as well asthat of the absorption probabilities along the boundaries.

Green functions for killed random walks in the Weyl chamber of Sp(4)