A point process describing the component sizes in the critical window of the random graph evolution
Probability
2007-05-23 v1 Combinatorics
Abstract
We study a point process describing the asymptotic behavior of sizes of the largest components of the random graph G(n,p) in the critical window p=n^{-1}+lambda n^{-4/3}. In particular, we show that this point process has a surprising rigidity. Fluctuations in the large values will be balanced by opposite fluctuations in the small values such that the sum of the values larger than a small epsilon is almost constant.
Cite
@article{arxiv.math/0505529,
title = {A point process describing the component sizes in the critical window of the random graph evolution},
author = {Svante Janson and Joel Spencer},
journal= {arXiv preprint arXiv:math/0505529},
year = {2007}
}
Comments
25 pages