Phase transitions in dynamical random graphs
(2006) In Journal of Statistical Physics 123(5). p.10071032 Abstract
 We study a largetime 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
 15729613
 DOI
 10.1007/s1095500691013
 language
 English
 LU publication?
 yes
 id
 ce5fb3abea444b48a25f21b96a359aaa (old id 399070)
 date added to LUP
 20160401 16:56:49
 date last changed
 20200112 19:53:31
@article{ce5fb3abea444b48a25f21b96a359aaa, abstract = {We study a largetime 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 = {15729613}, language = {eng}, number = {5}, pages = {10071032}, publisher = {Springer}, series = {Journal of Statistical Physics}, title = {Phase transitions in dynamical random graphs}, url = {http://dx.doi.org/10.1007/s1095500691013}, doi = {10.1007/s1095500691013}, volume = {123}, year = {2006}, }