 The contact process on the complete graph with random vertex-dependent infection ratesJonathon Peterson Stochastic Processes and their Applications, 2011, vol. 121, issue 3, 609-629 Abstract: We study the contact process on the complete graph on n vertices where the rate at which the infection travels along the edge connecting vertices i and j is equal to [lambda]wiwj/n for some [lambda]>0, where wi are i.i.d. vertex weights. We show that when there is a phase transition at [lambda]c>0 such that for [lambda] [lambda]c the contact process lives for an exponential amount of time. Moreover, we give a formula for [lambda]c and when [lambda]>[lambda]c we are able to give precise approximations for the probability that a given vertex is infected in the quasi-stationary distribution. Our results are consistent with a non-rigorous mean field analysis of the model. This is in contrast to some recent results for the contact process on power law random graphs where the mean field calculations suggested that [lambda]c>0 when in fact [lambda]c=0. Keywords: Contact; process; Random; environment; Phase; transition (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:121:y:2011:i:3:p:609-629 Ordering information: This journal article can be ordered from Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
Is your work missing from RePEc? Here is how to contribute.
Questions or problems? Check the EconPapers FAQ or send mail to .
EconPapers is hosted by the
School of Business at Örebro University.