Large deviation theory applied to extreme waves

This talk discusses a probabilistic approach to extreme wave events that exploits the fact that extreme events are rare and therefore very unlikely to begin with. There is a substantial body of mathematical theory called `large deviation theory' that deals specifically with the occurence, likelihood, and shape of rare events.

If one were to summarize the main results of large deviation theory in just one sentence, one could say that events with very little likelihood, when they occur, do so in the overwhelmingly majority of cases by following the path that is least unlikely. In this sense, rare events of a stochastic process become nearly deterministic and very often this theory leads to unexpectedly nice and simple results that deserve to be more widely known.

Actually, some parts of the general theory have been rediscovered by oceanographers, but the general theory is not well known. This talk will give an introduction to how large deviation theory works and how it can be applied to oceanographic problems such as rogue surface waves or large internal waves that become unstable, break, and produce deep-ocean turbulent diffusion.