Asymptotics for the size of the largest component scaled to "logn" in inhomogeneous random graphs
(2013) In Arkiv för Matematik 51(2). p.371-403- Abstract
- We study inhomogeneous random graphs in the subcritical case. Among other results, we derive an exact formula for the size of the largest connected component scaled by logn, with n being the size of the graph. This generalizes a result for the "rank-1 case". We also investigate branching processes associated with these graphs. In particular, we discover that the same well-known equation for the survival probability, whose positive solution determines the asymptotics of the size of the largest component in the supercritical case, also plays a crucial role in the subcritical case. However, now it is the negative solutions that come into play. We disclose their relationship to the distribution of the progeny of the branching process.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/4027116
- author
- Turova, Tatyana LU
- organization
- publishing date
- 2013
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Arkiv för Matematik
- volume
- 51
- issue
- 2
- pages
- 371 - 403
- publisher
- Springer
- external identifiers
-
- wos:000323247000010
- scopus:84883824997
- ISSN
- 0004-2080
- DOI
- 10.1007/s11512-012-0178-4
- language
- English
- LU publication?
- yes
- id
- 0c86109f-74e9-41fa-ac51-86c7c6913a73 (old id 4027116)
- date added to LUP
- 2016-04-01 14:45:36
- date last changed
- 2022-01-28 02:25:44
@article{0c86109f-74e9-41fa-ac51-86c7c6913a73, abstract = {{We study inhomogeneous random graphs in the subcritical case. Among other results, we derive an exact formula for the size of the largest connected component scaled by logn, with n being the size of the graph. This generalizes a result for the "rank-1 case". We also investigate branching processes associated with these graphs. In particular, we discover that the same well-known equation for the survival probability, whose positive solution determines the asymptotics of the size of the largest component in the supercritical case, also plays a crucial role in the subcritical case. However, now it is the negative solutions that come into play. We disclose their relationship to the distribution of the progeny of the branching process.}}, author = {{Turova, Tatyana}}, issn = {{0004-2080}}, language = {{eng}}, number = {{2}}, pages = {{371--403}}, publisher = {{Springer}}, series = {{Arkiv för Matematik}}, title = {{Asymptotics for the size of the largest component scaled to "logn" in inhomogeneous random graphs}}, url = {{http://dx.doi.org/10.1007/s11512-012-0178-4}}, doi = {{10.1007/s11512-012-0178-4}}, volume = {{51}}, year = {{2013}}, }