Phase transitions in dynamical random graphs
(2006) In Journal of Statistical Physics 123(5). p.1007-1032- Abstract
- We study a large-time limit of a Markov process whose states are finite graphs. The number of the vertices is described by a supercritical branching process, and the dynamics of edges is determined by the rates of appending and deleting. We find a phase transition in our model similar to the one in the random graph model G (n,p). We derive a formula for the line of critical parameters which separates two different phases: one is where the size of the largest component is proportional to the size of the entire graph, and another one, where the size of the largest component is at most logarithmic with respect to the size of the entire graph. In the supercritical phase we find the asymptotics for the size of the largest component.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/399070
- author
- Turova, Tatyana LU
- organization
- publishing date
- 2006
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- inhomogeneous random graphs, phase transitions
- in
- Journal of Statistical Physics
- volume
- 123
- issue
- 5
- pages
- 1007 - 1032
- publisher
- Springer
- external identifiers
-
- wos:000239646800002
- scopus:33746890856
- ISSN
- 1572-9613
- DOI
- 10.1007/s10955-006-9101-3
- language
- English
- LU publication?
- yes
- id
- ce5fb3ab-ea44-4b48-a25f-21b96a359aaa (old id 399070)
- date added to LUP
- 2016-04-01 16:56:49
- date last changed
- 2022-01-28 23:17:25
@article{ce5fb3ab-ea44-4b48-a25f-21b96a359aaa, abstract = {{We study a large-time limit of a Markov process whose states are finite graphs. The number of the vertices is described by a supercritical branching process, and the dynamics of edges is determined by the rates of appending and deleting. We find a phase transition in our model similar to the one in the random graph model G (n,p). We derive a formula for the line of critical parameters which separates two different phases: one is where the size of the largest component is proportional to the size of the entire graph, and another one, where the size of the largest component is at most logarithmic with respect to the size of the entire graph. In the supercritical phase we find the asymptotics for the size of the largest component.}}, author = {{Turova, Tatyana}}, issn = {{1572-9613}}, keywords = {{inhomogeneous random graphs; phase transitions}}, language = {{eng}}, number = {{5}}, pages = {{1007--1032}}, publisher = {{Springer}}, series = {{Journal of Statistical Physics}}, title = {{Phase transitions in dynamical random graphs}}, url = {{http://dx.doi.org/10.1007/s10955-006-9101-3}}, doi = {{10.1007/s10955-006-9101-3}}, volume = {{123}}, year = {{2006}}, }