## Discrete Random Walks, DRW'03

### Cyril Banderier and Christian Krattenthaler (eds.)

### DMTCS Conference Volume AC (2003), pp. 95-104

author: | Rick Durrett |
---|---|

title: | Rigorous Result for the CHKN S Random Graph Model |

keywords: | random graph, clusterization, Brownian motion, singularity analysis |

abstract: | We study the phase transition in a random graph in which vertices and edges are added at constant rates. Two recent papers in Physical Review E by Callaway, Hopcroft, Kleinberg, Newman, and Strogatz, and Dorogovstev, Mendes, and Samukhin have computed the critical value of this model, shown that the fraction of vertices in finite clusters is infinitely differentiable at the critical value, and that in the subcritical phase the cluster size distribution has a polynomial decay rate with a continuously varying power. Here we sketch rigorous proofs for the first and third results and a new estimates about connectivity probabilities at the critical value. |

If your browser does not display the abstract correctly (because of the different mathematical symbols) you may look it up in the PostScript or PDF files. | |

reference: | Rick Durrett (2003), Rigorous
Result for the
CHKN
S Random Graph Model, in Discrete Random Walks,
DRW'03, Cyril Banderier and Christian Krattenthaler
(eds.), Discrete Mathematics and Theoretical Computer
Science Proceedings AC, pp. 95-104 |

bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |

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