Geodesic
A remark on the isomorphism between the Bernoulli scheme and the Plancherel measure
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXIX, Tome 468 (2018), pp. 98-104 
P. E. Naryshkin. A remark on the isomorphism between the Bernoulli scheme and the Plancherel measure. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXIX, Tome 468 (2018), pp. 98-104. http://geodesic.mathdoc.fr/item/ZNSL_2018_468_a8/
@article{ZNSL_2018_468_a8,
     author = {P. E. Naryshkin},
     title = {A remark on the isomorphism between the {Bernoulli} scheme and the {Plancherel} measure},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {98--104},
     year = {2018},
     volume = {468},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2018_468_a8/}
}
TY  - JOUR
AU  - P. E. Naryshkin
TI  - A remark on the isomorphism between the Bernoulli scheme and the Plancherel measure
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2018
SP  - 98
EP  - 104
VL  - 468
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2018_468_a8/
LA  - ru
ID  - ZNSL_2018_468_a8
ER  - 
%0 Journal Article
%A P. E. Naryshkin
%T A remark on the isomorphism between the Bernoulli scheme and the Plancherel measure
%J Zapiski Nauchnykh Seminarov POMI
%D 2018
%P 98-104
%V 468
%U http://geodesic.mathdoc.fr/item/ZNSL_2018_468_a8/
%G ru
%F ZNSL_2018_468_a8

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

We formulate a theorem of Romik and Śniady which establishes an isomorphism between the Bernoulli scheme and the Plancherel measure. Then we derive from it several combinatorial results. The first one is related to measurable partitions; the other two are related to the Knuth equivalence. We also give several examples and one conjecture belonging to A. M. Vershik.

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

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

[3] P. Śniady, “Robinson–Schensted–Knuth algorithm, jeu de taquin and Kerov–Vershik measures on infinite tableaux”, SIAM J. Discrete Math., 28:2 (2014), 598–630 | DOI | MR | Zbl

[4] S. V. Fomin, “Prilozhenie 1”: R. Stenli, Perechislitelnaya kombinatorika, v. 2, Mir, Moskva, 2009

[5] P. Flajolet, R. Sedgewick, Analytic Combinatorics, Cambridge Univ. Press, Cambridge, 2009 | MR | Zbl

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

[7] A. Vershik, “Ubyvayuschie posledovatelnosti izmerimykh razbienii i ikh prilozheniya”, DAN SSSR, 193:4 (1970), 748–751 | MR | Zbl