Skip to main content

Lund University Publications

LUND UNIVERSITY LIBRARIES

Phase transitions in dynamical random graphs

Turova, Tatyana LU (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:
author
organization
publishing date
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
2020-01-12 19:53:31
@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},
  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},
}