Record Statistics and Dynamics

The term record statistics covers the statistical properties of records within an ordered series of numerical data obtained from observations or measurements. A record within such series is simply a value larger (or smaller) than all preceding values. The mathematical properties of records strongly depend on the properties of the series from which they are extracted. These properties have been investigated for many different cases, the simplest cases perhaps being series of independent random numbers drawn from the same (arbitrary) distribution, and series produced by a diffusion process with independent random increments.

The term record dynamics covers the rather new idea that records may, in special situations, have measurable dynamical consequences. The approach applies to the aging dynamics of glasses and other systems with multiple metastable states. The basic idea is that record sizes fluctuations of e. g. the energy are able to push the system past some sort of ‘edge of stability’, inducing irreversible configurational changes, whose statistics then closely follows the statistics of record fluctuations.