Phase transitions in random graphs and coagulation processes.

Inhomogeneous random graphs are a natural generalization of the well-known Erdos–Renyi random graph, where vertices are characterized by a type and edges are present independently according to the type of the vertices that they are connecting. In the sparse regime, these graphs undergo a phase transition in terms of the emergence of a giant component exactly as the classical Erdos–Renyi model. We will present an alternative approach, via large deviations, to prove this phase transition. This allows a comparison with the gelationphase transition in coagulation processes and with phase transitions of condensation type emerging in several systems of interacting components.
This is based on ongoing joint works with Wolfgang K\"onig (WIAS and TUBerlin), Tejas Iyer (WIAS), Heide Langhammer (WIAS), Elena Magnanini(WIAS) and Robert Patterson (WIAS).