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

Raschel, Kilian

Annales de l'I.H.P. Probabilités et statistiques, Tome 47 (2011) no. 4, pp. 1001-1019.

Dans cet article, nous considérons une famille de marches aléatoires tuées au bord de la chambre de Weyl du dual de Sp(4), qui vérifie en outre la propriété suivante : pour tout n ≥ 3, il y a, dans cette famille, une marche ayant un groupe de réflexions d'ordre 2n. De plus, le cas n = 4 correspond à un processus bien connu apparaissant lors de l'étude des marches aléatoires quantiques sur le dual de Sp(4). Pour tous les processus de cette famille, nous trouvons l'asymptotique exacte des fonctions de Green selon toutes les trajectoires, ainsi que l'asymptotique des probabilités d'absorption sur le bord.

We consider a family of random walks killed at the boundary of the Weyl chamber of the dual of Sp(4), which in addition satisfies the following property: for any n ≥ 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 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.

Classification : 60G50, 31C35, 30E20, 30F10
Mots clés : killed random walk, Green functions, Martin boundary, absorption probabilities

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