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Interlaced processes on the circle

Anthony P. MetcalfeNeil O’ConnellJon Warren — 2009

Annales de l'I.H.P. Probabilités et statistiques

When two Markov operators commute, it suggests that we can couple two copies of one of the corresponding processes. We explicitly construct a number of couplings of this type for a commuting family of Markov processes on the set of conjugacy classes of the unitary group, using a dynamical rule inspired by the RSK algorithm. Our motivation for doing this is to develop a parallel programme, on the circle, to some recently discovered connections in random matrix theory between reflected and conditioned...

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