Geodesic
Combinatorial coding of Bernoulli schemes and asymptotics of Young tables
Funkcionalʹnyj analiz i ego priloženiâ, Tome 54 (2020) no. 2, pp. 3-24.

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A. M. Vershik. Combinatorial coding of Bernoulli schemes and asymptotics of Young tables. Funkcionalʹnyj analiz i ego priloženiâ, Tome 54 (2020) no. 2, pp. 3-24. http://geodesic.mathdoc.fr/item/FAA_2020_54_2_a0/

[1] A. M. Vershik, “Asimptotika razbieniya kuba na simpleksy Veilya i kodirovanie skhemy Bernulli”, Funkts. analiz i ego pril., 53:2 (2019), 11–31 | DOI | MR | Zbl

[2] S. V. Kerov, A. M. Vershik, “The characters of infinite symmetric group and probabilty properties of the Robinson–Shensted–Knuth algorithm”, SIAM J. Algebraic Discrete Methods, 7:1 (1986), 116–124 | DOI | MR | Zbl

[3] D. Romik, P. Sniady, “Jeu de taquin dynamics on infinite Young tableaux and second class particles”, Ann. Probab., 43:2 (2015), 682–737 | DOI | MR | Zbl

[4] P. Sniady, “Robinson–Shensted–Knuth algorithm, jeu de taquin and Kerov–Vershik measures on infinite tableaux”, JIAM J. Deiscrete Math., 28:2 (2014), 598–630 | MR | Zbl

[5] A. M. Vershik, “Ravnomernaya algebraicheskaya approksimatsiya operatorov sdviga i umnozheniya”, Dokl. AN SSSR, 259:3 (1981), 526–529 | MR | Zbl

[6] A. M. Vershik, “Teorema o markovskoi approksimatsii v ergodicheskoi teorii”, Zap. nauchn. semin. LOMI, 115 (1982), 72–82 | Zbl

[7] A. M. Vershik, “Tri teoremy edinstvennosti mery Plansherelya s raznykh pozitsii”, Trudy MIAN, 305 (2019), 71–85 | DOI | Zbl

[8] A. B. Gribov, “Predelnaya forma tablits Yunga otnositelno mery Plansherelya”, Vestnik LGU, Ser. matem., mekh., astron., 2 (1986), 100–102 | MR

[9] S. Kerov, G. Olshansky, A. Vershik, “Harmonic analysis on the infinite symmetric group”, Invent. Math., 158:3 (2004), 551–642 | DOI | MR | Zbl

[10] A. M. Bershik, “Problema kombinatornogo kodirovaniya nepreryvnoi dinamiki i ponyatie transfera na prostranstve putei grafa”, Zap. nauchn. sem. POMI, 481 (2019), 12–28

[11] A. M. Vershik, “Teoriya filtratsii podalgebr, standartnost i nezavisimost”, UMN, 72:2(434) (2017), 67–146 | DOI | MR | Zbl

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

[13] A. M. Vershik, S. V. Kerov, “Kharaktery i faktor-predstavleniya beskonechnoi simmetricheskoi gruppy”, Dokl. AN SSSR, 257:5 (1981), 1037–1040 | MR | Zbl

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

[15] D. Knuth, The Art of Computer Programming, Sorting and Searching, v. 3, Addison-Wesley, Reading, 1998 | MR

[16] A. Borodin, A. Okounkov, G. Olshansky, “Asymptotics of Plansherel measures for symmetric groups”, J. Amer. Math. Soc., 13:3 (2000), 481–515 | DOI | MR | Zbl

[17] J. Bike, P. Deift, K. Johansson, “On the ditribution of the length of the longest increasing subsequence of random permutations”, J. Amer. Math. Soc., 12:4 (1999), 1119–1178 | DOI | MR

[18] E. Glasner, B. Weiss, “The universal minimal system for the group of homeomorphisms of the Cantor set”, Fund. Math., 176:3 (2003), 277–289 | DOI | MR | Zbl

[19] A. M. Vershik, S. V. Kerov, “Kharaktery i faktor-predstavleniya beskonechnoi simmetricheskoi gruppy”, Dokl. AN SSSR, 257:5 (1981), 1037–1040 | MR | Zbl

[20] R. Stenli, Perechislitelnaya kombinatorika, Derevya, proizvodyaschie funktsii i simmetricheskie funktsii, Mir, M., 2005

[21] C. Fomin, “Prilozhenie 1 k gl. 7”: R. Stenli, Perechislitelnaya kombinatorika, Mir, M., 2005

[22] B. Logan, L. Shepp, “A variational problem for random Young tableaux”, Adv. Math., 26:2 (1977), 206–222 | DOI | MR | Zbl

[23] A. Vershik, N. Tsilevich, “The serpentine representation of the infinite symmetric group and the basic representation of the affine Lie algebra $\widehat{sl}_2$ Lett.”, Math. Phys., 105:1 (2015), 11–25 | MR | Zbl

[24] A. M. Vershik, N. V. Tsilevich, “Gruppy, porozhdennye involyutsiyami rombovidnykh grafov i deformatsii ortogonalnoi formy Yunga”, Zap. nauchn. sem. POMI., 481 (2019), 29–38

[25] A. Vershik, N. Tsilevich, “On different model of representation of infinite symmetric group”, Adv. Appl. Math., 37 (2006), 526–540 | DOI | MR | Zbl

[26] I. F. Azangulov, G. V. Ovechkin, “Otsenka vremeni popadaniya koordinaty skhemy Bernulli v pervyi stolbets tablitsy Yunga”, Funkts. analiz i ego pril., 54:2 (2020), 78–84 | DOI | MR | Zbl