Limit shape for regularisation of large partitions under the Plancherel measure
Representation Theory
2024-04-22 v2 Combinatorics
Metric Geometry
Probability
Abstract
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 -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 -regularisation.
Cite
@article{arxiv.2302.07115,
title = {Limit shape for regularisation of large partitions under the Plancherel measure},
author = {Salim Rostam},
journal= {arXiv preprint arXiv:2302.07115},
year = {2024}
}
Comments
37 pages, lots of figures. v2: We now prove that the limit shape is convex. The proof of the main theorem is now splitted throughout the paper and the organisation of the paper has changed accordingly