@article{doi:10.1002/rsa.20771,
author = {Stufler, Benedikt},
title = {Gibbs partitions: The convergent case},
journal = {Random Structures \& Algorithms},
year = {2018},
volume = {53},
number = {3},
pages = {537-558},
keywords = {Gibbs partitions, graph classes, graph limits, random graphs, random partitions of sets},
doi = {10.1002/rsa.20771},
url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/rsa.20771},
eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/rsa.20771},
abstract = {Abstract We study Gibbs partitions that typically form a unique giant component. The remainder is shown to converge in total variation toward a Boltzmann-distributed limit structure. We demonstrate how this setting encompasses arbitrary weighted assemblies of tree-like combinatorial structures. As an application, we establish smooth growth along lattices for small block-stable classes of graphs. Random graphs with n vertices from such classes are shown to form a giant connected component. The small fragments may converge toward different Poisson Boltzmann limit graphs, depending along which lattice we let n tend to infinity. Since proper addable minor-closed classes of graphs belong to the more general family of small block-stable classes, this recovers and generalizes results by McDiarmid (2009).}
}