  Inspired by reliability issues in electric transmission networks, we use a
probabilistic approach to study the occurrence of large failures in a stylized
cascading failure model. In this model, lines have random capacities that
initially meet the load demands imposed on the network. Every single line
failure changes the load distribution in the surviving network, possibly
causing further lines to become overloaded and trip as well. An initial single
line failure can therefore potentially trigger massive cascading effects, and
in this paper we measure the risk of such cascading events by the probability
that the number of failed lines exceeds a certain large threshold. Under
particular critical conditions, the exceedance probability follows a power-law
distribution, implying a significant risk of severe failures. We examine the
robustness of the power-law behavior by exploring under which assumptions this
behavior prevails.
