The phase transition in random graphs and coagulation processes: a large deviation approach
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. In the sparse regime, 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 Dr. Andreis 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 König (WIAS and TU Berlin), Robert Patterson (WIAS) and Heide
Luisa Andreis is a post-doc fellow at WAIS - Weierstrass Institute. Previously, she was research fellow at the University of Padova. She received her PhD in Mathematics from the University of Padova, Italy, in 2017. Her research
focuses on probability theory and interacting particle systems. Particularly, she is interested in coagulation
processes, condensation, gelation and phase transitions, interacting random walks and scaling limits, reinforced
processes, emergence of self-sustained periodic behaviour in cooperative systems, mean-field interacting particle
systems and propagation of chaos, large deviations.