Alexander Gnedin (QMUL)
The arrangement problem for Poisson-Dirichlet random measures and partitions
A stick-breaking construction of the (two-parameter) Poisson-Dirichlet
random measure yields the masses arranged in the size-biased order.
Another order, which may be called `regenerative',
appears when the masses are associated with jumps of a transformed
increasing Levy process.
For Ewens' subfamily these orders coincide, but in general
the relation is more delicate.
In this talk we show how the orders can be constructively linked to one another
by means of a parametric family
of infinite random permutations.
A similar problem is also discussed in terms of integer partitions
induced by drawing a finite sample from the Poisson-Dirichlet distribution.