Pure Maths Colloquium: Mark Holland

Record events occur in many situations, such as in temperature records within weather, financial asset price records, and in sporting events, e.g. the 100m sprint. Within probability and random processes, the study of records can be formalised and their limit distributions studied. If we take a sequence of random variables \(X_1,\ldots, X_n\), a record time corresponds to the time \(t\) event where we have \(X_t>\max\left(X_1,\ldots, X_{t-1}\right)\), i.e. \(X_t\) exceeds all values occurring before time \(t\). A topic of interest is the distribution of such record times, and corresponding record values. In the talk, we review classical results which are part of a wider extreme value theory. We consider first processes that are independent, and identically distributed. Then we mention recent progress when the process \((X_n)\) is generated by a dynamical system.