The critical random graph, with martingales

Asaf Nachmias; Yuval Peres

The critical random graph, with martingales

概率论 2011-11-10 v4 组合数学

作者: Asaf Nachmias , Yuval Peres

摘要

We give a short proof that the largest component of the random graph $G(n, 1/n)$ is of size approximately $n^{2/3}$ . The proof gives explicit bounds for the probability that the ratio is very large or very small.

关键词

random graphs percolation theory probability theory

引用

@article{arxiv.math/0512201,
  title  = {The critical random graph, with martingales},
  author = {Asaf Nachmias and Yuval Peres},
  journal= {arXiv preprint arXiv:math/0512201},
  year   = {2011}
}

备注

13 pages, 1 figure. Revised version. Contains stronger probability deviation bounds and handles the entire scaling window. To appear in Israel Journal of Mathematics

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