Shirshendu Chatterjee: Asymptotic Behavior of Aldous' Gossip Process

Aldous (2007) defined a gossip process in which space is a discrete torus of size N, and the state of the process at time t is the set of individuals who know the information. Information spreads from a site to its nearest neighbors at rate 1/4 each and at rate N^{-\alpha} to a site chosen at random from the torus. We will be interested in the case in which \alpha < 3, where the long range transmission significantly accelerates the time at which everyone knows the information. We prove three results that precisely describe the spread of information and asymptotic behavior of the cover time in a slightly simplified model on the (real) torus.