Stochastic invertible mappings between power law and Gaussian probability distributions

C. Vignat; A. Plastino

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arXiv · cond-mat/0504709

Stochastic invertible mappings between power law and Gaussian probability distributions

C. Vignat·A. Plastino

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Abstract

We construct "stochastic mappings" between power law probability distributions (PD's) and Gaussian ones. To a given vector $N$, Gaussian distributed (respectively $Z$, exponentially distributed), one can associate a vector $X$, "power law distributed", by multiplying $X$ by a random scalar variable $a$, $N= a X$. This mapping is "invertible": one can go via multiplication by another random variable $b$ from $X$ to $N$ (resp. from $X$ to $Z$), i.e., $X=b N$ (resp. $X=b Z$). Note that all the above equalities mean "is distributed as". As an application of this stochastic mapping we revisit the so-called "zero-th law of thermodynamics problem" that bedevils the practitioners of nonextensive thermostatistics.

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C. Vignat, A. Plastino. 2005-04-27. Stochastic invertible mappings between power law and Gaussian probability distributions. https://arxiv.org/abs/cond-mat/0504709

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