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- W4300421868 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 demon- strate 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)." @default.
- W4300421868 created "2022-10-03" @default.
- W4300421868 creator A5080408565 @default.
- W4300421868 date "2016-09-28" @default.
- W4300421868 modified "2023-09-26" @default.
- W4300421868 title "Gibbs partitions: the convergent case" @default.
- W4300421868 doi "https://doi.org/10.48550/arxiv.1609.08859" @default.
- W4300421868 hasPublicationYear "2016" @default.
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