Georgia Institute of Technology College of Sciences

Random graphs are the basic mathematical models for large-scale disordered networks in many different fields (e.g., physics, biology, sociology). Their systematic study was pioneered by Erdoes and Renyi around 1960, and one key feature of many classical models is that the edges appear independently. While this makes them amenable to a rigorous analysis, it is desirable (both mathematically and in terms of applications) to understand more complicated situations. In this talk I will discuss some of my work on so-called Achlioptas processes, which (i) are evolving random graph models with dependencies between the edges and (ii) give rise to more interesting percolation phase transition phenomena than the classical Erdoes-Renyi model.