  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.
