Merging Percolation on Z(d) and Classical Random Graphs: Phase Transition
(2010) In Random Structures & Algorithms 36(2). p.185-217- Abstract
- We study a random graph model which is a superposition of bond percolation on Z(d) with parameter p, and a classical random graph G(n,c/n). We show that this model, being a homogeneous random graph, has a natural relation to the so-called "rank I case" of inhomogeneous random graphs. This allows us to use the newly developed theory of inhomogeneous random graphs to describe the phase diagram on the set of parameters c >= 0 and 0 <= p < p(c), where p(c) = p(c)(d) is the critical probability for the bond percolation on Z(d). The phase transition is of second order as in the classical random graph. We find the scaled size of the largest connected component in the supercirtical regime. We also provide a sharp upper bound for the... (More)
- We study a random graph model which is a superposition of bond percolation on Z(d) with parameter p, and a classical random graph G(n,c/n). We show that this model, being a homogeneous random graph, has a natural relation to the so-called "rank I case" of inhomogeneous random graphs. This allows us to use the newly developed theory of inhomogeneous random graphs to describe the phase diagram on the set of parameters c >= 0 and 0 <= p < p(c), where p(c) = p(c)(d) is the critical probability for the bond percolation on Z(d). The phase transition is of second order as in the classical random graph. We find the scaled size of the largest connected component in the supercirtical regime. We also provide a sharp upper bound for the largest connected component in the subcritical regime. The latter is a new result for inhomogeneous random graphs with unbounded kernels. (C) 2009 Wiley Periodicals, Inc. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1568788
- author
- Turova, Tatyana LU and Vallier, Thomas LU
- organization
- publishing date
- 2010
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- inhomogeneous random graphs, percolation, phase transition
- in
- Random Structures & Algorithms
- volume
- 36
- issue
- 2
- pages
- 185 - 217
- publisher
- John Wiley & Sons Inc.
- external identifiers
-
- wos:000274458400003
- scopus:74349124266
- ISSN
- 1098-2418
- DOI
- 10.1002/rsa.20287
- language
- English
- LU publication?
- yes
- id
- 5e94ac8d-e283-4c85-8700-afc8d7bccdb0 (old id 1568788)
- date added to LUP
- 2016-04-01 09:48:12
- date last changed
- 2022-01-25 08:53:11
@article{5e94ac8d-e283-4c85-8700-afc8d7bccdb0,
abstract = {{We study a random graph model which is a superposition of bond percolation on Z(d) with parameter p, and a classical random graph G(n,c/n). We show that this model, being a homogeneous random graph, has a natural relation to the so-called "rank I case" of inhomogeneous random graphs. This allows us to use the newly developed theory of inhomogeneous random graphs to describe the phase diagram on the set of parameters c >= 0 and 0 <= p < p(c), where p(c) = p(c)(d) is the critical probability for the bond percolation on Z(d). The phase transition is of second order as in the classical random graph. We find the scaled size of the largest connected component in the supercirtical regime. We also provide a sharp upper bound for the largest connected component in the subcritical regime. The latter is a new result for inhomogeneous random graphs with unbounded kernels. (C) 2009 Wiley Periodicals, Inc.}},
author = {{Turova, Tatyana and Vallier, Thomas}},
issn = {{1098-2418}},
keywords = {{inhomogeneous random graphs; percolation; phase transition}},
language = {{eng}},
number = {{2}},
pages = {{185--217}},
publisher = {{John Wiley & Sons Inc.}},
series = {{Random Structures & Algorithms}},
title = {{Merging Percolation on Z(d) and Classical Random Graphs: Phase Transition}},
url = {{http://dx.doi.org/10.1002/rsa.20287}},
doi = {{10.1002/rsa.20287}},
volume = {{36}},
year = {{2010}},
}