Sparse inhomogeneous random graphs from a large deviation point of view

10.05.2021, 14:00
Forschungsseminar Wahrscheinlichkeitstheorie

Luisa Andreis (Uni. Firenze)

Inhomogeneous  random  graphs  are  a  natural  generalization  of  the  well-known Erdös 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 Erdös-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 some coagulation process and with phase transitions of condensation type emerging in several systems of interacting components. This  is  an  ongoing  joint  work  with  W. König  (WIAS  and  TU  Berlin), R. Patterson (WIAS) and H. Langhammer (WIAS Berlin).

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