Leopold Infeld Colloquium

Extreme fluctuations or events are often associated with power law statistics. Indeed, it is a popular belief that "wild randomness" (to use a term proposed by Mandelbrot) is deeply associated with distributions with power law tails characterized by small exponents. In other words, power law tails are often seen as the epitome of extreme events. Here, we document in several systems that there is life beyond power law tails: power laws can be superseded by "dragons", monster events that occur beyond the power law tail. Dragons reveal hidden mechanisms that are only transiently active and that amplify the normal power law fluctuations. We will present evidence of the dragon phenomenon on the statistics of financial losses, hydrodynamic turbulence, material rupture, earthquakes, epileptic seizures, and cyber risks. The special status of dragons open a new research program on their predictability, based on the hypothesis that they belong to a different class of their own and express specific mechanisms amplifying the normal dynamics via positive feedbacks. We will present evidence of these claims for the predictions of material rupture, earthquakes, financial crashes and epileptic seizures. The dragon approach allows us to understand the present World financial crisis as underpinned by two decades of successive financial and economic bubbles. We will demonstrate how market risk management can be enlarged by combining strategic, tactical and time-varying risk analysis.