LA Probability Forum (3/3)

One of the most interesting features of finite random graphs is the `percolation phase transition', where the global structure intuitively changes from only small components to a single giant component plus small ones. In this talk we discuss the percolation phase transition in the several time-evolving random graph models (where, starting with an empty graph on n vertices, new random edges are added step-by-step according to certain rules or restrictions). The proofs are based on an interplay between discrete and continuous methods, and we will highlight connections to ideas and heuristics arising in percolation theory as well as aggregation and coagulation theory, including the usage of differential equations and partial differential equations. Based on joint work with Oliver Riordan, Nick Wormald and Laura Eslava, respectively.