On the variational problem for upper tails in sparse random graphs

@article{Lubetzky2017OnTV,
  title={On the variational problem for upper tails in sparse random graphs},
  author={Eyal Lubetzky and Y. Zhao},
  journal={Random Struct. Algorithms},
  year={2017},
  volume={50},
  pages={420-436}
}
  • Eyal Lubetzky, Y. Zhao
  • Published 2017
  • Mathematics, Computer Science
  • Random Struct. Algorithms
  • What is the probability that the number of triangles in Gn,p, the Erdi¾?s-Renyi random graph with edge density p, is at least twice its mean? Writing it as exp[-rn,p], already the order of the rate function rn, p was a longstanding open problem when p=o1, finally settled in 2012 by Chatterjee and by DeMarco and Kahn, who independently showed that rn,pi¾?n2p2log1/p for pi¾?lognn; the exact asymptotics of rn, p remained unknown. The following variational problem can be related to this large… CONTINUE READING
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    References

    SHOWING 1-10 OF 33 REFERENCES
    On replica symmetry of large deviations in random graphs
    • 71
    • PDF
    A Large Deviation Result On The Number Of Small Subgraphs Of A Random Graph
    • V. Vu
    • Computer Science, Mathematics
    • Comb. Probab. Comput.
    • 2001
    • 70
    • PDF
    Quick Approximation to Matrices and Applications
    • 441
    • Highly Influential
    The large deviation principle for the Erdős-Rényi random graph
    • 135
    • Highly Influential
    Random Graphs
    • 2,042
    • PDF
    The infamous upper tail
    • 122
    The Deletion Method For Upper Tail Estimates
    • 55
    • PDF
    Large Networks and Graph Limits
    • L. Lovász
    • Mathematics, Computer Science
    • Colloquium Publications
    • 2012
    • 482
    • PDF
    Upper tails for subgraph counts in random graphs
    • 103
    • PDF