Gibbs fragmentation trees

By Peter McCullagh, Jim Pitman, Matthias Winkel. 2007

47 citations recorded by the source corpus.

We study fragmentation trees of Gibbs type. In the binary case, we identify the most general Gibbs type fragmentation tree with Aldous’s beta-splitting model, which has an extended parameter range � > −2 with respect to the beta(� + 1,� + 1) probability distributions on which it is based. In the multifurcating case, we show that Gibbs fragmentation trees are associated with the two-parameter Poisson-Dirichlet models for exchangeable random partitions of N, with an extended parameter range 0 ≤ � ≤ 1, � ≥ −2� and � < 0, � = −m�, m ∈ N.

Subfields: Artificial Intelligence, Condensed Matter Physics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/63ce07f4db759ea0491902bec8b687b1f9a3d50a

Citations in the corpus

• A new family of Markov branching trees: the alpha-gamma model (2008, unknown): “It was shown in [19] that Aldous’s beta-splitting models for β > − 2 are the only binary Markov branching models for which the EPPF is of Gibbs type and that the multifurcating Gibbs models are an extended Ewens-Pitman two-parameter family of random partitions, 0 ≤ α ≤ 1, θ ≥ − 2 α , or −∞ ≤ α 0,…”