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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A. M. Vershik and S. V. Kerov, “Asymptotic theory of characters of the symmetric group,” Funct. Anal. Appl., 15, 246–255 (1982).
A. M. Borodin, “Multiplicative central measures on the Schur graph,” J. Math. Sci. (N.Y.), 96, No. 5, 3472–3477 (1999).
S. V. Kerov, “A differential model of the growth of Young diagrams,” Amer. Math. Soc. Transl. Ser. 2, 188, 111–130 (1999).
A. M. Vershik and D. Pavlov, “Numerical experiments in problems of asymptotic representation theory,” J. Math. Sci. (N.Y.), 168, No. 3, 351–361 (2010).
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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