Abstract:

Sparse inhomogeneous random graphs are a natural generalization of the well-known Erdos Rényi random graph, where vertices are characterized by a type and edges are independent but distributed according to the type of the vertices that they are connecting. These graphs undergo a phase transition in terms of the emergence of a giant component exactly as the classical Erdos Rényi model. In this talk we will present an alternative approach, via large deviations, to prove this phase transition. This allows a comparison with the gelation phase transition that characterizes coagulation processes and the phase transition of condensation type emerging in several systems of interacting components. This is an ongoing joint work with Wolfgang Koenig (WIAS and TU Berlin), Robert Patterson (WIAS) and Heide Langhammer (TU Berlin).