ON SCALING AND REGULAR VARIATION

Abstract

We survey scaling arguments, both asymptotic (involving regular variation) and exact (involving self-similarity), in various areas of mathemat- ical analysis and mathematical physics. 1. Scaling and Fechner's law There is a sizeable body of theory to the effect that, where two related physically meaningful functions f and g have no natural scale in which to measure their units, and are reasonably smooth, then their relationship is given by a power law: (F)