### Phase transitions in random graphs and coagulation processes.

Probability Seminar

25th March 2022, 3:30 pm – 4:30 pm

Fry Building, 2.04 (also on zoom)

Inhomogeneous random graphs are a natural generalization of the well known Erdős–Rényi 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 Erdős–Rényi model. We will present an alternative approach, via large deviations, to prove this phase transition. This allows a comparison with the gelation phase 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 Kőnig (WIAS and TU Berlin), Tejas Iyer (WIAS), Heide Langhammer (WIAS), Elena Magnanini (WIAS) and Robert Patterson (WIAS).

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