Year: 2026
Type: preprint
Abstract: We study pairs of labeled random partitions $(Π,τ)$ with a finite label set $E$, which can be thought of as a random mutation and coalescence mechanism of a countable number of blocks. Labeled exchangeable partition probability functions (LEPPFs) are defined via labeled analogues of Kingman's paintbox partitions. They satisfy normalization, symmetry and consistency in a multivariate sense. Under an equivariance condition, a representation for $(Π,τ)$ in terms of labeled paintbox partitions is derived, leading to a full characterization of LEPPFs by a unique probability measure $G$. This representation is extended to jointly exchangeable and consistent transition pairs using a product measure $F \otimes G$. These results yield a one-to-one correspondence between distributions of jointly exchangeable and consistent transition pairs and pairs of exchangeable distributions and LEPPFs.
Source: arXiv (Cornell University)
Authors: Flamm, Maximilian, Möhle, Martin
Institution: University of Tübingen
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223232227