Numerical experiments in problems of asymptotic representation theory
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XVII, Tome 373 (2009), pp. 77-93 Cet article a éte moissonné depuis la source Math-Net.Ru

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The article presents the results of experiments in computation of statistical values related to Young diagrams, including the estimates on maximum and average (by Plancherel distribution) dimension of irreducible representation of symmetric group $S_n$. The computed limit shapes of two-dimensional and three-dimensional diagrams distributed by Richardson statistics are presented as well. Bibl. – 14 titles.
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A. M. Vershik; D. Pavlov. Numerical experiments in problems of asymptotic representation theory. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XVII, Tome 373 (2009), pp. 77-93. http://geodesic.mathdoc.fr/item/ZNSL_2009_373_a4/

[1] U. Fulton, Tablitsy Yunga i ikh prilozheniya k teorii predstavlenii i geometrii, MTsNMO, Moskva, 2006

[2] A. M. Vershik, A. Yu. Okunkov, “Induktivnyi podkhod k postroeniyu teorii predstavlenii simmetricheskikh grupp”, Uspekhi matematicheskikh nauk, 51:2(308) (1996), 153–154 | DOI | MR | Zbl

[3] A. M. Vershik, S. V. Kerov, “Asimptotika mery Plansherelya simmetricheskoi gruppy i predelnaya forma tablits Yunga”, DAN SSSR, 233:6 (1977), 1024–1027 | MR | Zbl

[4] A. M. Vershik, S. V. Kerov, “Asimptotika maksimalnoi i tipichnoi razmernostei neprivodimykh predstavlenii simmetricheskoi gruppy”, Funktsionalnyi analiz i ego prilozheniya, 19:1 (1985), 25–36 | MR | Zbl

[5] H. Rost, “Nonequilibrium behavior of a many particle process: Density profile and local equilibria”, Probability Theory and Related Fields, 58:1 (1981), 41–53 | MR | Zbl

[6] A. M. Vershik, A. B. Gribov, S. V. Kerov, “Eksperimenty po vychisleniyu razmernosti tipichnogo predstavleniya simmetricheskoi gruppy”, Zap. nauchn. semin. LOMI, 123, 1983, 152–154 | MR

[7] D. E. Knut, Iskusstvo programmirovaniya, Tom 3, vtoroe izdanie, Vilyams, Moskva, 2000

[8] A. M. Vershik, N. V. Tsilevich, “Induced representations of the infinite symmetric group”, Pure Appl. Math. Quart., 3:4 (2007), 1005–1026 | DOI | MR | Zbl

[9] R. M. Baer, P. Brock, “Natural Sorting over Permutation Spaces”, Math. Comp., 22 (1968), 385–410 | DOI | MR

[10] J. McKay, “The Largest Degrees of Irreducible Characters of the Symmetric Group”, Math. Comp., 30:135 (1976), 624–631 | DOI | MR | Zbl

[11] D. Richardson, “Random growth in a tesselation”, Proc. Cambridge Phil. Soc., 74 (1973), 515–528 | DOI | MR | Zbl

[12] A. Vershik, Yu. Yakubovich, “Fluctuation of maximal particle energy of quantum ideal gas and random partitions”, Comm. Math. Phys., 261:3 (2006), 759–769 | DOI | MR | Zbl

[13] R. Cerf, R. Kenyon, “The Low-Temperature Expansion of the Wulff Crystal in the 3D Ising Model”, Communications in Mathematical Physics, 222:1 (2001), 147–179 | DOI | MR | Zbl

[14] A. Okounkov, N. Reshetikhin, “Correlation function of Schur process with application to local geometry of a random 3-dimensional Young diagram”, J. Amer. Math. Soc., 16 (2003), 581–603 | DOI | MR | Zbl