GENERALIZED LEVY DISTRIBUTIONS AND THE PRINCIPLE OF COMPLEMENTARITY

Extreme value distributions are obtained from the normal distribution through a transformation that retains the concavity of the correspondi ng entropy reduction. By randomization of the conjugate variable, a qu asistable law is converted into a strictly stable law, which is a gene ralization of Levy's distribution. A principle of complementarity is e stablished generalizing Levy's discovery of the complementarity betwee n random displacements, parametrized by time, and random time, paramet rized by position, in the description of Brownian motion. The statisti cal distribution in line broadening is shown to be derived from the no rmal distribution for the largest value in the volume, centered about a radiating atom that does not contain a perturber, rather than from t he nearest neighbor distribution for the smallest distance between per turber and a radiating atom.