The article is devoted to the study of the asymptotics of the probabilities of paths in a certain Markov process on the 3D Young graph. We introduce a normalized dimension of paths and study the growth and oscillations of normalized dimensions along greedy trajectories of this process using computer experiments. Bibliography: 9 titles.
Similar content being viewed by others
References
A. M. Vershik and S. V. Kerov, “Asymptotic behavior of the maximum and generic dimensions of irreducible representations of the symmetric group,” Funct. Anal. Appl., 19, No. 1, 21–31 (1985).
V. S. Duzhin and N. N. Vasilyev, “Asymptotic behavior of normalized dimensions of standard and strict Young diagrams – growth and oscillations,” J. Knot Theory Ramifications, 26 (2016).
A. M. Vershik and S. V. Kerov, “Asymptotic theory of characters of the symmetric group,” Funct. Anal. Appl., 15, No. 4, 246–255 (1981).
L. Petrov, “Random walks on strict partitions,” J. Math. Sci., 168, No. 3, 437–463 (2010).
M. Nazarov, “Young’s orthogonal form of irreducible projective representations of the symmetric group,” J. London Math. Soc., 42, 437–451 (1990).
A. Borodin, “Multiplicative central measures on the Schur graph,” J. Math. Sci., 96, No. 5, 3472–3477 (1999).
N. N. Vasiliev and A. B. Terentjev, “Modelling of almost central measures generated by Markov processes in the three-dimensional case,” J. Math. Sci., 209, No. 6, 851–859 (2015).
A. Vershik and D. Pavlov, “Numerical experiments in problems of asymptotic representation theory,” J. Math. Sci., 168, 351–361 (2010).
N. N. Vasilyev and V. S. Duzhin, “Building irreducible representations of a symmetric group S(n) with large and maximum dimensions,” Inform.-uprav. sistemy, No. 3, 17–22 (2016).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 448, 2016, pp. 69–79.
Translated by the authors.
Rights and permissions
About this article
Cite this article
Vasiliev, N.N., Duzhin, V.S. Numerical Study of the Asymptotics of Path Probabilities in a Markov Process Close to a Central One on the 3D Young Graph. J Math Sci 224, 214–220 (2017). https://doi.org/10.1007/s10958-017-3406-4
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-017-3406-4