Friday, December 11, 2009

Power Law and an Enrico Fermi's motivation

Power Laws are very frequent in data mining. For instance, you can find a power law in many properties of the web graph. I found a quite interesting explanation of power laws for modelling particles and cosmic radiation (Enrico Fermi 1949)

In this model, particles are produced at constant rate and the particles' distribution at time t is an exponential of the form \lamda * e ^ - (\lamda * t) (in other words there is a negative exponential contribution). In addition, particles gain energy when time is passing such as C e ^ (\alpha * t) (in other words this is giving a positive exponential contribution).

Under these two forces the particles will have a power law density. Can you explain why?

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