We describe some computer experiments with 3D Young diagrams for modelling a Markov process whose properties are close to those of the Plancherel growth process in the two-dimensional case. The transition probabilities of this process are defined by formulas involving the lengths of 3D hooks. They were obtained by generalizing well-known formulas for the probabilities of the Plancherel growth process. Although the measure generated by this 3D Markov process is not central, we show that it is close to a central measure.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 432, 2015, pp. 68–82.
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Vasiliev, N.N., Terentjev, A.B. Modelling of Almost Central Measures Generated by Markov Processes in the Three-Dimensional Case. J Math Sci 209, 851–859 (2015). https://doi.org/10.1007/s10958-015-2532-0
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DOI: https://doi.org/10.1007/s10958-015-2532-0