Probability Seminar: Anna Levit

We study the behavior of the so-called quantum random graphs inside the "scaling window". The quantum random graphs were first introduced by Ioffe and Levit in 2007 and they turn to be a certain generalization of the Erdős–Rényi random graphs. We show results for the quantum random graphs which are analogous to those of Aldous (1997), who proved that inside the "critical window", the rescaled sizes of components of the Erdős–Rényi graphs converge to lengths of excursions of a certain process related to Brownian motion.