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

Kilian Raschel

Annales de l'I.H.P. Probabilités et statistiques (2011)

  • Volume: 47, Issue: 4, page 1001-1019
  • ISSN: 0246-0203

Abstract

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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.

How to cite

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Raschel, Kilian. "Green functions for killed random walks in the Weyl chamber of Sp(4)." Annales de l'I.H.P. Probabilités et statistiques 47.4 (2011): 1001-1019. <http://eudml.org/doc/239760>.

@article{Raschel2011,
abstract = {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.},
author = {Raschel, Kilian},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {killed random walk; Green functions; Martin boundary; absorption probabilities},
language = {eng},
number = {4},
pages = {1001-1019},
publisher = {Gauthier-Villars},
title = {Green functions for killed random walks in the Weyl chamber of Sp(4)},
url = {http://eudml.org/doc/239760},
volume = {47},
year = {2011},
}

TY - JOUR
AU - Raschel, Kilian
TI - Green functions for killed random walks in the Weyl chamber of Sp(4)
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2011
PB - Gauthier-Villars
VL - 47
IS - 4
SP - 1001
EP - 1019
AB - 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.
LA - eng
KW - killed random walk; Green functions; Martin boundary; absorption probabilities
UR - http://eudml.org/doc/239760
ER -

References

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