Limiting densities for small paramter contact processes in power law random graphs

2011. június 30. csütörtök, 17:15 (!!)

This is joint work with Valesin and Yao. We follow Chatterjee and Durrett in considering the contact process with infection parameter λ on a random graph where vertices have (essentially) an i.i.d. degree with law where the tail probabilities decay as a power. Surprisingly and in contrast to the physics predictions Chaterjee and Durrett showed that for power parameter a > 3 for any λ > 0 no matter how small, there was a non zero "density" for the random graph with probability tending to one as the size tends to infinity. We resolve open questions by identifying this limiting density and treating the case a > 2. Three regimes are shown: 2 < a < 2 1/2, 2 1/2 < a < 3 and a > 3.