Gibbs distributions for random partitions generated by a fragmentation process
| dc.creator | Berestycki, Nathanael | |
| dc.creator | Pitman, Jim | |
| dc.date | 2005-12-15 | |
| dc.date | 2006-11-14 | |
| dc.date.accessioned | 2026-07-07T06:55:23Z | |
| dc.date.available | 2026-07-07T06:55:23Z | |
| dc.description | In this paper we study random partitions of 1,...n, where every cluster of size j can be in any of w\_j possible internal states. The Gibbs (n,k,w) distribution is obtained by sampling uniformly among such partitions with k clusters. We provide conditions on the weight sequence w allowing construction of a partition valued random process where at step k the state has the Gibbs (n,k,w) distribution, so the partition is subject to irreversible fragmentation as time evolves. For a particular one-parameter family of weight sequences w\_j, the time-reversed process is the discrete Marcus-Lushnikov coalescent process with affine collision rate K\_{i,j}=a+b(i+j) for some real numbers a and b. Under further restrictions on a and b, the fragmentation process can be realized by conditioning a Galton-Watson tree with suitable offspring distribution to have n nodes, and cutting the edges of this tree by random sampling of edges without replacement, to partition the tree into a collection of subtrees. Suitable offspring distributions include the binomial, negative binomial and Poisson distributions. | |
| dc.description | 38 pages, 2 figures, version considerably modified. To appear in the Journal of Statistical Physics | |
| dc.identifier | https://arxiv.org/abs/math/0512378 | |
| dc.identifier | http://arxiv.org/abs/math/0512378 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/106261 | |
| dc.subject | Probability | |
| dc.subject | Statistical Mechanics | |
| dc.subject | Combinatorics | |
| dc.subject | MSC: 60J10, 60K35, 05A15, 05A19 | |
| dc.title | Gibbs distributions for random partitions generated by a fragmentation process | |
| dc.type | text |