Critical random hypergraphs: The emergence of a giant set of identifiable vertices
成果类型：
Article
署名作者：
Goldschmidt, C
署名单位：
Sorbonne Universite; Universite Paris Cite
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/009117904000000847
发表日期：
2005
页码：
1573-1600
关键词：
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 on component sizes in a random graph.