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The Incipient Giant Component in Bond Percolation on General Finite Weighted Graphs

Probability 2016-04-25 v1

Abstract

On a large finite connected graph let edges ee become "open" at independent random Exponential times of arbitrary rates wew_e. Under minimal assumptions, the time at which a giant component starts to emerge is weakly concentrated around its mean.

Keywords

Cite

@article{arxiv.1604.06741,
  title  = {The Incipient Giant Component in Bond Percolation on General Finite Weighted Graphs},
  author = {David J. Aldous},
  journal= {arXiv preprint arXiv:1604.06741},
  year   = {2016}
}