4 problems

Let $G$ be a simple, connected graph, and let an exceedance tie-breaking rule $T$ be used in the cascading-failure process described by Theorem. Tie-breaking independence conjectur…

Graph-scale-free-failure conjecture. Whenever a graph $G=(V,E)$ satisfies these two properties, the number of edge failures $A_G$ exhibits scale-free behavior. The conjecture propo…

Brownian-bridge failure-tail conjecture. The probability that the failure size in the giant component exceeds $\kappa(k)$ behaves like the probability that this Brownian bridge sta…

Total-load-surge conjecture. The total load surge is likely to be close to $i/m + \Theta(1/\sqrt{m})$ upon failure. This heuristic is used in the regime where the threshold is line…