Martin Boundary Theory of some Quantum Random Walks

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dc.creatorCollins, Benoit
dc.date2002-11-22
dc.date.accessioned2026-07-07T06:33:05Z
dc.date.available2026-07-07T06:33:05Z
dc.descriptionIn this paper we define a general setting for Martin boundary theory associated to quantum random walks, and prove a general representation theorem. We show that in the dual of a simply connected Lie subgroup of U(n), the extremal Martin boundary is homeomorphic to a sphere. Then, we investigate restriction of quantum random walks to Abelian subalgebras of group algebras, and establish a Ney-Spitzer theorem for an elementary random walk on the fusion algebra of SU(n), generalizing a previous result of Biane. We also consider the restriction of a quantum random walk on $SU_q(n)$ introduced by Izumi to two natural Abelian subalgebras, and relate the underlying Markov chains by classical probabilistic processes. This result generalizes a result of Biane.
dc.description29 pages
dc.identifierhttps://arxiv.org/abs/math/0211356
dc.identifierhttp://arxiv.org/abs/math/0211356
dc.identifierAnnales de l'IHP, Vol 40, 3:367--384 (2004).
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/99080
dc.subjectProbability
dc.subjectMathematical Physics
dc.subject31C35; 46L53
dc.titleMartin Boundary Theory of some Quantum Random Walks
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