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July 2005 Critical random hypergraphs: The emergence of a giant set of identifiable vertices
Christina Goldschmidt
Ann. Probab. 33(4): 1573-1600 (July 2005). DOI: 10.1214/009117904000000847


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 N2/3). 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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Christina Goldschmidt. "Critical random hypergraphs: The emergence of a giant set of identifiable vertices." Ann. Probab. 33 (4) 1573 - 1600, July 2005.


Published: July 2005
First available in Project Euclid: 1 July 2005

zbMATH: 1076.60010
MathSciNet: MR2150199
Digital Object Identifier: 10.1214/009117904000000847

Primary: 60C05
Secondary: 05C65 , 05C80 , 60F17

Keywords: Giant component , Identifiability , phase transition , Random hypergraphs

Rights: Copyright © 2005 Institute of Mathematical Statistics


Vol.33 • No. 4 • July 2005
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