TAMU Department of Statistics
Avalanches in an Excitable Network
I will discuss a propagation of avalanches in a complex network. “Avalanches” here is a general term describing a cascading spread of a “damage” in a network of linked objects. Examples of avalanches in applications include epidemics, outages in a power grid, rumors in a social network, neural cascades in cortex, viruses in a computer network, forest fire etc. Two types of heuristic approximation are frequently used for models of this type in applications, branching process approximation for cascades of a small size at the beginning of the process and a deterministic dynamical system once the avalanche spreads to a significant fraction of a large network. I am going to present several results concerning the exact relation between the avalanche model and these limits, including rates of convergence and rigorous bounds for common characteristics of the model. For instance, the widely used branching approximation is in essence a linearization, it is monotone in all basic parameters while the original model isn’t. Loosely speaking, some of our results can be viewed as a “second order” correction to the branching approximation.
Friday, 3/29/2019, 11:30 AM, BLOC 113