Quantum random walk on the dual of SU\((n)\) (Q1814300)

In the paper a quantum Markov chain on the group von Neumann algebra \(M\) of \(\text{SU}(n)\) is constructed and the restriction of this quantum Markov chain to the algebra of a maximal torus of \(\text{SU}(n)\) as a random walk on the lattice of integral forms of \(\text{SU}(n)\) with respect to this maximal torus is interpreted. Moreover, the restriction of this quantum Markov chain to the center of \(M\) is a Markov chain on the same lattice obtained from the preceding one by conditioning it (in Doob's sense) to exit a Weyl chamber by a Martin boundary point at \(\infty\).