Dear Colleagues, we would like to invite you to the following Probability seminar that will take place at the Department of Mathematics of Padova, on January 31. ________________________________________________________

Speaker: Alessandra Cipriani (TU Delft)

Title: Dynamical fitness models: evidence of universality classes for preferential attachment

31 JANUARY (Friday), 11:30; ROOM 1BC45, Dipartimento di Matematica “Tullio Levi-Civita”, Via Trieste 63, Padova

Abstract: In this talk we study different variations of a particular class of random graphs called preferential attachment models with fitness. These are dynamic graphs in which, at every time step, a new node attaches itself to an older one with probability proportional to the degree and a random factor associated to the node, called the fitness. Motivated by learning mechanisms of real-life networks, we assume the fitness to be a Moving Average process MA(q) with positive increments. We study different properties of such models, for example the degree distribution, the attachment probability and the phenomenon of Bose-Einstein condensation. Finally we provide evidence that, tuning the parameters of the fitness process, we fall into two universality classes represented by the well-known Albert-Barabàsi model and Bianconi-Barabàsi model. This implies the robustness of heavy tails in the degree distribution under random perturbations of the attachment rule.

All of you are very welcome.

Best regards, Alessandra Bianchi