On the largest component of a random graph with a subpower-law degree sequence in a subcritical phase
| dc.creator | Pittel, B. G. | |
| dc.date | 2008-08-21 | |
| dc.date.accessioned | 2026-07-07T09:57:41Z | |
| dc.date.available | 2026-07-07T09:57:41Z | |
| dc.description | A uniformly random graph on $n$ vertices with a fixed degree sequence, obeying a $γ$ subpower law, is studied. It is shown that, for $γ>3$, in a subcritical phase with high probability the largest component size does not exceed $n^{1/γ+\varepsilon_n}$, $\varepsilon_n=O(\ln\ln n/\ln n)$, $1/γ$ being the best power for this random graph. This is similar to the best possible $n^{1/(γ-1)}$ bound for a different model of the random graph, one with independent vertex degrees, conjectured by Durrett, and proved recently by Janson. | |
| dc.description | Published in at http://dx.doi.org/10.1214/07-AAP493 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/0808.2907 | |
| dc.identifier | http://arxiv.org/abs/0808.2907 | |
| dc.identifier | Annals of Applied Probability 2008, Vol. 18, No. 4, 1636-1650 | |
| dc.identifier | doi:10.1214/07-AAP493 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/167432 | |
| dc.subject | Probability | |
| dc.subject | 60C05, 60K35, 60J10 (Primary) | |
| dc.title | On the largest component of a random graph with a subpower-law degree sequence in a subcritical phase | |
| dc.type | text |