Titolo della tesi: Disordered models on sparse random graphs
The understanding of complex systems is a fundamental problem at the basis of many branches of human knowledge. In this thesis we aim to study some instances of complexity belonging to the realm of statistical physics of disordered systems. We focus on two models defined on sparse graphs, namely the random matching problem and the Ising spin glass, observing that sparsity may lead to macroscopic properties that are dramatically different from those exhibited on the fully-connected graph.