View abstract

Session S06 - Interacting Stochastic Systems

Tuesday, July 13, 12:00 ~ 12:35 UTC-3

The contact process on random hyperbolic graphs

Daniel Valesin

University of Groningen, The Netherlands   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloakf926cf50b7c2dc27043cdb3930199260').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addyf926cf50b7c2dc27043cdb3930199260 = 'd.r&#111;dr&#105;g&#117;&#101;s.v&#97;l&#101;s&#105;n' + '&#64;'; addyf926cf50b7c2dc27043cdb3930199260 = addyf926cf50b7c2dc27043cdb3930199260 + 'r&#117;g' + '&#46;' + 'nl'; var addy_textf926cf50b7c2dc27043cdb3930199260 = 'd.r&#111;dr&#105;g&#117;&#101;s.v&#97;l&#101;s&#105;n' + '&#64;' + 'r&#117;g' + '&#46;' + 'nl';document.getElementById('cloakf926cf50b7c2dc27043cdb3930199260').innerHTML += '<a ' + path + '\'' + prefix + ':' + addyf926cf50b7c2dc27043cdb3930199260 + '\'>'+addy_textf926cf50b7c2dc27043cdb3930199260+'<\/a>';

We consider the contact process on a random graph embedded in hyperbolic space (introduced by Krioukov, Papadopoulos, Kitsak, Vahdat and Boguñá in 2010), in the regime where the degree distribution obeys a power law with finite mean and infinite second moment. We show that the process exhibits metastable behavior (prolonged persistence of the infection) regardless of the value of the infection rate $\lambda$. We also find that the exponent of the metastable infection density when $\lambda$ is close to zero. This coincides with the the corresponding quantity for the contact process on another random graph (namely, the configuration model with power law degree distribution), suggesting universality of this exponent.

Joint work with Amitai Linker (University of Cologne, Germany), Dieter Mitsche (University of Lyon, France) and Bruno Schapira (Aix-Marseille Université, France).