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We give an algorithmic-bijective proof of Macdonald's reduced word identityin the theory of Schubert polynomials, in the special case where thepermutation is dominant. Our bijection uses a novel application of DavidLittle's generalized bumping algorithm. We also describe a Markov growthprocess for an associated probability distribution on reduced words. Our growthprocess can be implemented efficiently on a computer and allows for fastsampling of reduced words. We also discuss various partial generalizations andlinks to Little's work on the RSK algorithm.

A Markov growth process for Macdonald's distribution on reduced words