Unlabelled Gibbs partitions. (4th March 2020)

• Record Type: Journal Article
• Authors: Stufler, Benedikt
• Is Part Of: Combinatorics, probability and computing. Volume 29:Number 2(2020)
• Page Start: 293
• Page End: 309
• Publication Date: 2020-03-04
• Subjects: 60C05, -- 05A18, -- 60B10; Combinatorial analysis -- Periodicals; Probabilities -- Periodicals; Computer science -- Mathematics -- Periodicals; 511.6
• DOI: 10.1017/S0963548319000336
• Languages: English
• ISSNs: 0963-5483

Abstract

Abstract: We study random composite structures considered up to symmetry that are sampled according to weights on the inner and outer structures. This model may be viewed as an unlabelled version of Gibbs partitions and encompasses multisets of weighted combinatorial objects. We describe a general setting characterized by the formation of a giant component. The collection of small fragments is shown to converge in total variation toward a limit object following a Pólya–Boltzmann distribution.