The p-sphere and the geometric substratum of power law probability distributions
C. Vignat, A. Plastino
Abstract
Links between power law probability distributions and marginal distributions of uniform laws on p-spheres in Rn show that a mathematical derivation of the Boltzmann-Gibbs distribution necessarily passes through power law ones. Results are also given that link parameters p and n to the value of the non-extensivity parameter q that characterizes these power laws in the context of non-extensive statistics.
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