Merging Percolation on Z(d) and Classical Random Graphs: Phase Transition
(2010) In Random Structures & Algorithms 36(2). p.185217 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 socalled "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 socalled "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:
http://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
 external identifiers

 wos:000274458400003
 scopus:74349124266
 ISSN
 10982418
 DOI
 10.1002/rsa.20287
 language
 English
 LU publication?
 yes
 id
 5e94ac8de2834c858700afc8d7bccdb0 (old id 1568788)
 date added to LUP
 20100317 12:25:11
 date last changed
 20180107 03:01:01
@article{5e94ac8de2834c858700afc8d7bccdb0, 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 socalled "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 = {10982418}, keyword = {inhomogeneous random graphs,percolation,phase transition}, language = {eng}, number = {2}, pages = {185217}, publisher = {John Wiley & Sons}, 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}, volume = {36}, year = {2010}, }