Largest Components in Random Hypergraphs

@article{Cooley2018LargestCI,
  title={Largest Components in Random Hypergraphs},
  author={Oliver Cooley and Mihyun Kang and Yury Person},
  journal={Combinatorics, Probability and Computing},
  year={2018},
  volume={27},
  pages={741 - 762}
}
In this paper we consider j-tuple-connected components in random k-uniform hypergraphs (the j-tuple-connectedness relation can be defined by letting two j-sets be connected if they lie in a common edge and considering the transitive closure; the case j = 1 corresponds to the common notion of vertex-connectedness). We show that the existence of a j-tuple-connected component containing Θ(nj) j-sets undergoes a phase transition and show that the threshold occurs at edge probability $$\frac{(k-j… 
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