Records in a changing world

Abstract: Record-breaking events of all kinds generate considerable attention in the public domain, but the mathematical theory of records appears to be known only to specialists. In its classic form, the theory is concerned with records in time series of independent, identically distributed random variables. In recent work we have extended the basic record model by taking into account a systematic, linear time dependence of the mean of the underlying random variables. Applications of the theory to global warming and stock market fluctuations will be described, and it will be explained why the drift induces correlations between record events.