A first order phase transition in the threshold θ≥2 contact process on random r-regular graphs and r-trees
AbstractWe consider the discrete time threshold-θ contact process on a random r-regular graph. We show that if θ≥2, r≥θ+2, ϵ1 is small and p≥p1(ϵ1), then starting from all vertices occupied the fraction of occupied vertices is ≥1−2ϵ1 up to time exp(γ1(r)n) with high probability. We also show that for p2<1 there is an ϵ2(p2)>0 so that if p≤p2 and the initial density is ≤ϵ2(p2), then the process dies out in time O(logn). These results imply that the process on the r-tree has a first-order phase transition.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Elsevier in its journal Stochastic Processes and their Applications.
Volume (Year): 123 (2013)
Issue (Month): 2 ()
Contact details of provider:
Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description
You can help add them by filling out this form.
reading list or among the top items on IDEAS.Access and download statisticsgeneral information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.