临界随机超图：可识别顶点巨集的出现
Critical random hypergraphs: The emergence of a giant set of identifiable vertices
摘要：
我们考虑一个模型的随机超图的可识别性，一个模拟的连通性。当底层随机图变得临界时，该模型在可识别顶点的比例中具有相变。相变采取各种形式，这取决于控制不同类型的超边缘的参数的值。它可以是连续的，就像在随机图中一样。(In事实上，当没有高阶边时，这正是巨分支的出现。）在这种情况下，存在一系列可能的"组件“大小（包括但不限于N^{2/3}）。或者，相变可以是不连续的。我们特别感兴趣的性质的不连续相变，并能够表现出精确的渐近。我们的方法扩展了Aldous [Ann. Probab. 25（1997）812-854]中关于随机图中的分量大小。
英文摘要：
We consider a model for random hypergraphs with identifiability, an analogue of connectedness. This model has a phase transition in the proportion of identifiable vertices when the underlying random graph becomes critical. The phase transition takes various forms, depending on the values of the parameters controlling the different types of hyperedges. It may be continuous as in a random graph. (In fact, when there are no higher-order edges, it is exactly the emergence of the giant component.) In this case, there is a sequence of possible sizes of ``components'' (including but not restricted to N^{2/3}). Alternatively, the phase transition may be discontinuous. We are particularly interested in the nature of the discontinuous phase transition and are able to exhibit precise asymptotics. Our method extends a result of Aldous [Ann. Probab. 25 (1997) 812-854] on component sizes in a random graph.
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