Dynamical Systems Seminar

Given a sequence of random variables X₁, X₂, ..., one is interested in the behavior of M_n=max(X₁, ..., X_n) as n grows. Knowing this gives, for example, the likelihood of a "catastrophic" event (i.e., an outcome whose value exceeds a particular threshold).

For IID (Independent Identically Distributed) random variables, the limit distribution of the (rescaled) maxima is well understood. We are interested in the case when X_n are successive measurements of a dynamical system (a "time series"). We show that under some hyperbolicity assumptions, the limit behavior is the same as for IID observations.

I will explain the IID results, and describe the methods we use in the more general setting. The necessary Probability Theory notions will also be explained.

This is joint work with Mark Holland (University of Exeter) and Matthew Nicol.