Contact processes on random graphs with power law degree distributions have critical value 0.

@inproceedings{Chatterjee2009ContactPO,
  title={Contact processes on random graphs with power law degree distributions have critical value 0.},
  author={Shirshendu Chatterjee and Rick Durrett},
  year={2009}
}
If we consider the contact process with infection rate λ on a random graph on n vertices with power law degree distributions, mean field calculations suggest that the critical value λc of the infection rate is positive if the power α > 3. Physicists seem to regard this as an established fact, since the result has recently been generalized to bipartite graphs by Gómez-Gardeñes et al (2008). Here, we show that the critical value λc is zero for any value of α > 3, and the contact process, starting… CONTINUE READING

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