Modeling rare events in complex systems
Unlikely events matter. Massive earthquakes, giant hurricanes, global ?nancial crises, and pandemics are just a few examples of events that are rare but have catastrophic consequences. There are also many other situations in which the occurrence of a rare event is less dramatic but important nonetheless: for instance, typical electronic components are required to be extremely reliable, with a very low probability of failure, as are many other engineering devices used in the automobile, aerospace, and medical industries. In all of these examples, it is desirable to accurately estimate the (small) probability of occurrence of rare events. This, however, is a nontrivial question that has received substantial attention recently. In this talk, I will review mathematical tools that are available in this context as well as numerical methods that can be built upon these tools.