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We provide two new constructions of Markov chains which had previously arisenfrom the representation theory of the infinite-dimensional unitary group. Thefirst construction uses the combinatorial rule for the Littlewood-Richardsoncoefficients, which arise from tensor products of irreducible representationsof the unitary group. The second arises from a quantum random walk on the groupvon Neumann algebra of U(n), which is then restricted to the center.Additionally, the restriction to a maximal torus can be expressed in terms ofweight multiplicities, explaining the presence of tensor products.

Two constructions of Markov chains on the dual of U(n)