Characterizations of exchangeable partitions and random discrete distributions by deletion properties

Details Characterizations of exchangeable partitions and random discrete distributions by deletion properties Characterizations of exchangeable partitions and random discrete distributions by deletion properties

2009-09-20

arxiv.org/abs/0909.3642v2

Mathematics

Probability

29 pages

Scientific paper

We prove a long-standing conjecture which characterises the Ewens-Pitman two-parameter family of exchangeable random partitions, plus a short list of limit and exceptional cases, by the following property: for each $n = 2,3, >...$, if one of $n$ individuals is chosen uniformly at random, independently of the random partition $\pi_n$ of these individuals into various types, and all individuals of the same type as the chosen individual are deleted, then for each $r > 0$, given that $r$ individuals remain, these individuals are partitioned according to $\pi_r'$ for some sequence of random partitions $(\pi_r')$ that does not depend on $n$. An analogous result characterizes the associated Poisson-Dirichlet family of random discrete distributions by an independence property related to random deletion of a frequency chosen by a size-biased pick. We also survey the regenerative properties of members of the two-parameter family, and settle a question regarding the explicit arrangement of intervals with lengths given by the terms of the Poisson-Dirichlet random sequence into the interval partition induced by the range of a neutral-to-the right process.

Affiliated with

Also associated with

No associations

Rating

Characterizations of exchangeable partitions and random discrete distributions by deletion properties does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Characterizations of exchangeable partitions and random discrete distributions by deletion properties, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Characterizations of exchangeable partitions and random discrete distributions by deletion properties will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-296350