Core size of a random partition for the Plancherel measure
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866910415841132544 |
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| author | Rostam, Salim |
| author_facet | Rostam, Salim |
| contents | 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 infinity 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 goes to infinity, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_05970 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Core size of a random partition for the Plancherel measure Rostam, Salim Probability Combinatorics Representation Theory 60C05 (Primary) 41A60, 05E10 (Secondary) 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 infinity 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 goes to infinity, 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. |
| title | Core size of a random partition for the Plancherel measure |
| topic | Probability Combinatorics Representation Theory 60C05 (Primary) 41A60, 05E10 (Secondary) |
| url | https://arxiv.org/abs/2111.05970 |