Geodesic
Kerov's central limit theorem for Schur-Weyl and Gelfand measures (extended abstract)
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) (2011).

Voir la notice de l'article provenant de la source Episciences

We show that the shapes of integer partitions chosen randomly according to Schur-Weyl measures of parameter $\alpha =1/2$ and Gelfand measures satisfy Kerov's central limit theorem. Thus, there is a gaussian process $\Delta$ such that under Plancherel, Schur-Weyl or Gelfand measures, the deviations $\Delta_n(s)=\lambda _n(\sqrt{n} s)-\sqrt{n} \lambda _{\infty}^{\ast}(s)$ converge in law towards $\Delta (s)$, up to a translation along the $x$-axis in the case of Schur-Weyl measures, and up to a factor $\sqrt{2}$ and a deterministic remainder in the case of Gelfand measures. The proofs of these results follow the one given by Ivanov and Olshanski for Plancherel measures; hence, one uses a "method of noncommutative moments''. 
@article{DMTCS_2011_special_260_a56,
     author = {M\'eliot, Pierre-Lo{\"\i}c},
     title = {Kerov's central limit theorem for {Schur-Weyl} and {Gelfand} measures (extended abstract)},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)},
     year = {2011},
     doi = {10.46298/dmtcs.2943},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2943/}
}
TY  - JOUR
AU  - Méliot, Pierre-Loïc
TI  - Kerov's central limit theorem for Schur-Weyl and Gelfand measures (extended abstract)
JO  - Discrete mathematics & theoretical computer science
PY  - 2011
VL  - DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2943/
DO  - 10.46298/dmtcs.2943
LA  - en
ID  - DMTCS_2011_special_260_a56
ER  - 
%0 Journal Article
%A Méliot, Pierre-Loïc
%T Kerov's central limit theorem for Schur-Weyl and Gelfand measures (extended abstract)
%J Discrete mathematics & theoretical computer science
%D 2011
%V DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2943/
%R 10.46298/dmtcs.2943
%G en
%F DMTCS_2011_special_260_a56
Méliot, Pierre-Loïc. Kerov's central limit theorem for Schur-Weyl and Gelfand measures (extended abstract). Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) (2011). doi : 10.46298/dmtcs.2943. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2943/

Cité par Sources :