The continuum limit of critical random graphs
| dc.creator | Addario-Berry, Louigi | |
| dc.creator | Broutin, Nicolas | |
| dc.creator | Goldschmidt, Christina | |
| dc.date | 2009-03-27 | |
| dc.date | 2009-05-06 | |
| dc.date.accessioned | 2026-07-07T13:11:46Z | |
| dc.date.available | 2026-07-07T13:11:46Z | |
| dc.description | We consider the Erdos-Renyi random graph G(n,p) inside the critical window, that is when p=1/n+ lambda*n^{-4/3}, for some fixed lambda in 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. | |
| dc.description | 34 pages, 5 figures | |
| dc.identifier | https://arxiv.org/abs/0903.4730 | |
| dc.identifier | http://arxiv.org/abs/0903.4730 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/229386 | |
| dc.subject | Probability | |
| dc.subject | Combinatorics | |
| dc.title | The continuum limit of critical random graphs | |
| dc.type | text |