The contact process on random hyperbolic graphs: metastability and critical exponents

We consider the contact process on the model of hyperbolic random graph, in the regime when the degree distribution obeys a power law with exponent $chi in(1,2)$ (so that the degree distribution has finite mean and infinite second moment). We show that the probability of non-extinction as the rate of infection goes to zero decays as a power law with an exponent that only depends on $chi$ and which is the same as in the configuration model, suggesting some universality of this critical exponent. We also consider fini