Interevent time distribution in seismicity: a theoretical approach

This paper presents an analysis of the distribution of the time $\tau$ between two consecutive events in a stationary point process. The study is motivated by the discovery of a unified scaling law for $\tau$ for the case of seismic events. It is shown that the unified law must necessarily be exponential. We discuss the parameterization of the empirical unified law and the physical meaning of the parameters involved.