Dynamical Systems Seminar

For dynamical systems we discuss the statistics of extremes, namely the statistical limit laws that govern the process \(M_{n}=\max\{X_1,X_2,\ldots,X_n\}\) , where \(X_i\) correspond to a stationary time series of observations generated by the dynamical system. We discuss extreme statistics for a range of examples of interest to those working in ergodic theory and chaotic dynamical systems. In a work in progress, we also discuss the statistics of records, namely the distribution of times \(n\) such that \(X_{n}=M_n\), and the distribution of the corresponding record values. [For the latter we will review the I.I.D. case first.]