Limit shape for regularisation of large partitions under the Plancherel measure

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 $e$-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.

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