Stochastic invertible mappings between power law and Gaussian probability distributions

Details Stochastic invertible mappings between power law and Gaussian probability distributions Stochastic invertible mappings between power law and Gaussian probability distributions

2005-04-27

arxiv.org/abs/cond-mat/0504709v1

Physics

Condensed Matter

Statistical Mechanics

9 pages

Scientific paper

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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