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The $p-$sphere and the geometric substratum of power law probability distributions

C. Vignat·A. Plastino
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Abstract

Links between power law probability distributions and marginal distributions of uniform laws on $p$-spheres in $\mathbb{R}^{n}$ 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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C. Vignat, A. Plastino. 2005-05-06. The $p-$sphere and the geometric substratum of power law probability distributions. https://doi.org/10.1016/j.physleta.2005.05.027

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