Universalidade, fractalidade, processos difusivos e maratonas: física além da física

Abstract

The aim of this work is the analysis of the distribution of time intervals t measured among participants who cross the finish line consecutively in marathons and half marathons. More specifically, if ti is the finish time of the i-th finisher, the time interval between him or her and the next one will be t = ti+1 ti, i = 1, ..., N 1. N is the finishers total number. After analysing di↵erent set of data, we verified that the distribuition is of power law type N(t) / t (1+↵) , with ↵ ⇡ 1.2. Our study used data set from marathons and half marathons across several countries and years. Besides the power law encountered, two other results that we consider relevant are the fact that the distributions show the same universality class, that is, the same exponent, and that it is invariant in space and time, meaning that it is independent of the place and year of the event. We believe that the same procedure can be applied to di↵erent competitions.