Gabriele Taricco
Modelling opinion dynamics on large-scale networks by Boltzmann-type kinetic equations and graphons.
Rel. Andrea Tosin. Politecnico di Torino, Corso di laurea magistrale in Ingegneria Matematica, 2026
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Abstract
This thesis explores the asymptotic behaviour of opinion dynamics on large-scale, heterogeneous networks. To overcome the computational and theoretical challenges posed by the increasing complexity due to the copious amounts of agent interactions, we employ the theory of graphons (graph functions) to describe the network topology in a continuous limit. A central contribution of this work is the rigorous derivation of a kinetic model that generalizes classical spatially homogeneous frameworks to topologically complex settings: by embedding the discrete node set into a continuous domain, we establish the convergence of the discrete particle system to its continuous limit in the W_1 Wasserstein metric, ensuring that the macroscopic description faithfully retains the structural information of the underlying graph.
Moreover, we investigate the analytical characterization of the stationary states of the system
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