03/11/2021, 17:00 — 18:00 — Sala P3.10, Pavilhão de Matemática Online
Luisa Andreis, University of Florence
Phase transition in sparse random graphs and coagulation processes
Inhomogeneous random graphs are a natural generalization of the wellknown Erdös-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 Erd}os{R enyi 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 some coagulation process and with phase transitions of condensation type emerging in several systems of interacting components. This is an ongoing joint work with Wolfgang Koenig (WIAS and TU Berlin), Tejas Iyer (WIAS), Heide Langhammer (WIAS), Robert Patterson (WIAS).
