Probability Theory and Related Fields

, Volume 89, Issue 1, pp 117-129

First online:

Quantum random walk on the dual of SU (n)

  • Philippe BianeAffiliated withLaborative de probabilités, Tour 56-66, 3e étage, Université Paris 6

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We study a quantum random walk onA(SU(n)), the von Neumann algebra of SU(n), obtained by tensoring the basic representation of SU(n). Two classical Markov chains are derived from this quantum random walk, by restriction to commutative subalgebras ofA(SU(n)), and the main result of the paper states that these two Markov chains are related by means of Doob'sh-processes.