Exponential Extinction Time of the Contact Process on Rank-One Inhomogeneous Random Graphs
- 115 Downloads
We show that the contact process on the rank-one inhomogeneous random graphs and Erdos–Rényi graphs with mean degree large enough survives a time exponential in the size of these graphs for any positive infection rate. In addition, a metastable result for the extinction time is also proved.
KeywordsContact process Inhomogeneous random graphs Erdos–Rényi random graphs Extinction time
Mathematics Subject Classification (2010)82C22 05C80
I am grateful to Bruno Schapira for his help and suggestions during the preparation of this work. I wish to thank also the anonymous referee for carefully reading the manuscript and many valuable comments. This work is supported by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant number 101.03–2017.07.
- 2.Berger, N., Borgs, C., Chayes, J.T., Saberi, A.: On the spread of viruses on the internet. In: Proceedings of the Sixteenth Annual ACM-SIAM symposium on discrete algorithms, pp. 301–310 (2005)Google Scholar
- 8.Can, V.H.: Metastability for the contact process on the preferential attachment graph, accepted for publication in Internet Mathematics. doi: 10.24166/im.08.2017
- 11.van der Hofstad, R.: Random graphs and complex networks. http://www.win.tue.nl/~rhofstad/NotesRGCN.html