Location of Repository

Distributional limits for critical random graphs

By L. Addario-berry, N. Broutin and C. Goldschmidt

Abstract

We consider the Erdős–Rényi random graph G(n, p) inside the critical window, that is when p = 1/n + λn −4/3, for some fixed λ ∈ R. Then, as a metric space with the graph distance rescaled by n −1/3, the sequence of connected components G(n, p) converges towards a sequence of continuous compact metric spaces. The result relies on a bijection between graphs and certain marked random walks, and the theory of continuum random trees. Our result gives access to the answers to a great many questions about distances in critical random graphs. In particular, we deduce that the diameter of G(n, p) rescaled by n −1/3 converges in distribution to an absolutely continuous random variable with finite mean. Keywords: Random graphs, Gromov-Hausdorff distance, scaling limits, continuum random tree, diameter. 2000 Mathematics subject classification: 05C80, 60C05

Year: 2009
OAI identifier: oai:CiteSeerX.psu:10.1.1.184.1465
Provided by: CiteSeerX
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • http://citeseerx.ist.psu.edu/v... (external link)
  • http://algo.inria.fr/broutin/p... (external link)
  • Suggested articles


    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.