Computer Science/Discrete Mathematics Seminar II

Motivated in part by various sequences of graphs growing under random rules (like internet models), convergent sequences of dense graphs and their limits were introduced by Borgs, Chayes, Lovasz, Sos and Vesztergombi and by Lovasz and Szegedy. In the talk we use this framework to study one of the motivating class of examples, namely randomly growing graphs. We prove the (almost sure) convergence of several such randomly growing graph sequences, and determine their limit. The analysis is not always straightforward: in some cases the cut distance from a limit object can be directly estimated, in other case densities of subgraphs can be shown to converge. Joint work with Christian Borgs, Jennifer Chayes, Laszlo Lovasz, Vera Sos, K.V.