Core size of a random partition for the Plancherel measure
Core size of a random partition for the Plancherel measure
Abstract : We prove that the size of the e-core of a partition taken under the Poissonised Plancherel measure converges in distribution to, as the Poisson parameter goes to +∞ and after a suitable renormalisation, a sum of e − 1 mutually independent Gamma distributions with explicit parameters. Such a result already exists for the uniform measure on the set of partitions of n as n → +∞, the parameters of the Gamma distributions being all equal. We rely on the fact that the descent set of a partition is a determinantal point process under the Poissonised Plancherel measure and on a central limit theorem for such processes.
https://hal.archives-ouvertes.fr/hal-03426306
Contributeur : Salim Rostam Connectez-vous pour contacter le contributeur
Soumis le : vendredi 12 novembre 2021 - 10:42:41
Dernière modification le : vendredi 20 mai 2022 - 09:04:51
Contributeur : Salim Rostam Connectez-vous pour contacter le contributeur
Soumis le : vendredi 12 novembre 2021 - 10:42:41
Dernière modification le : vendredi 20 mai 2022 - 09:04:51
Fichier
2111.05970.pdf
Fichiers produits par l'(les) auteur(s)