Dear all,

We are glad to announce the second seminar of the *Torino seminar series in Stochastics and Mathematical Statistics. *

Torino seminar series SMS is a monthly seminar series held at the Department of Mathematics G. Peano of the University of Turin. For more info and a list of future talks see https://sites.google.com/view/torinostochastics.

*Date and time:** Tuesday 9 November*, 2021, h 14:30-15:30

*Location*: Aula 5, Palazzo Campana, via Carlo Alberto 10, Torino

*Speaker*: *Luisa ANDREIS *(University of Florence)

*Title*: Phase transition in sparse random graphs and coagulation processes.

*Abstract**:* 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. 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 König (WIAS and TU Berlin), Tejas Iyer (WIAS), Heide Langhammer (WIAS), Robert Patterson (WIAS).

Best regards, The organizers (Tiziano De Angelis, Giuseppe D'Onofrio, Elena Issoglio)