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

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

2009-10-22

arxiv.org/abs/0910.4355v2

Ann. Inst. H. Poincar\'e Probab. Statist. 47 (2011) 1001-1019

Mathematics

Probability

20 pages

Scientific paper

We consider a family of random walks killed at the boundary of the Weyl chamber of the dual of $\rm{Sp}(4)$, which in addition satisfies the following property: for any $n\geq 3$, there is in this family a walk associated with a reflection group of order $2n$. Moreover, the case $n=4$ corresponds to a process 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 exact asymptotic of the Green functions along all infinite paths of states as well as that of the absorption probabilities along the boundaries.

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