Limit shape for regularisation of large partitions under the Plancherel measure
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866910414840791040 |
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| author | Rostam, Salim |
| author_facet | Rostam, Salim |
| contents | A celebrated result of Kerov-Vershik and Logan-Shepp gives an asymptotic shape for large partitions under the Plancherel measure. We prove that when we consider $e$-regularisations of such partitions we still have a convex limit shape, which is given by a shaking of the Kerov-Vershik-Logan-Shepp curve. We deduce an explicit form for the first asymptotics of the length of the first rows and the first columns for the $e$-regularisation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_07115 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Limit shape for regularisation of large partitions under the Plancherel measure Rostam, Salim Representation Theory Combinatorics Metric Geometry Probability 05E10, 20C30, 52A10 (Primary) 60F05 (Secondary) A celebrated result of Kerov-Vershik and Logan-Shepp gives an asymptotic shape for large partitions under the Plancherel measure. We prove that when we consider $e$-regularisations of such partitions we still have a convex limit shape, which is given by a shaking of the Kerov-Vershik-Logan-Shepp curve. We deduce an explicit form for the first asymptotics of the length of the first rows and the first columns for the $e$-regularisation. |
| title | Limit shape for regularisation of large partitions under the Plancherel measure |
| topic | Representation Theory Combinatorics Metric Geometry Probability 05E10, 20C30, 52A10 (Primary) 60F05 (Secondary) |
| url | https://arxiv.org/abs/2302.07115 |