Three Aspects of Life on a Random Graph

• Activity Number: 384
• Type: Invited
• Date/Time: Tuesday, August 3, 2010 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Computing
• Author(s): Rick Durrett*+
• Companies: Cornell University

Abstract

Random graphs are useful models of social networks so it is important to understand how processes behave on them. In this talk we will discuss three examples, each of which is joint work with either Daniel Remenik or Shirshendu Chatterjee. In the first we consider the contact process on a power law random graph and show that, in contrast to what physicists think, the critical value is always 0 for any power. In the second, we will consider a model for the spread of gypsy moths which alternates contact process growth and epidemics, finding chaotic behavior of the densities. Finally, we consider random Boolean networks, abstractions of gene networks, and show they have a transition from an orderly to a chaotic phase.