A point process describing the component sizes in the critical window of the random graph evolution
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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 May 2005
 DOI:
 10.48550/arXiv.math/0505529
 arXiv:
 arXiv:math/0505529
 Bibcode:
 2005math......5529J
 Keywords:

 Mathematics  Probability;
 Mathematics  Combinatorics;
 60C05;
 60K99;
 05C80
 EPrint:
 25 pages