Relatore: Dott. Marcello MussoLuogo: Sala Feynman - Plesso FisicoE-mail organizzatore: marisa.bonini@fis.unipr.itAbstract: Distribution and correlation properties of dark matter halos probe important features of the standard model of our Universe,such as the relative abundance of its constituents (through their redshift dependence) and the deviation from Gaussianity ofits initial conditions (through their scale dependence).I will present recent developments of the so-called excursion set theory, which uses random walks to make simple – yetremarkably accurate - analytical predictions for halo statistics, and compare them with simulations.