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.

中文翻译：

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未标记的 Gibbs 分区

我们研究了考虑到对称性的随机复合结构，这些结构根据内部和外部结构的权重进行采样。该模型可以被视为 Gibbs 分区的未标记版本，并包含多组加权组合对象。我们描述了一个以形成一个巨大组件为特征的一般环境。小碎片的集合显示出按照 Pólya-Boltzmann 分布以总变化向极限对象收敛。