Stochastic invertible mappings for Tsallis distributions

We devise mappings between Gaussian distributions and power-law distributions, nowadays also called Tsallis distributions. To a given Tsallis distributed vector X, one can associate a Gaussian distributed vector N in the fashion N = a X where a is a random variable independent of X whose properties we are going to characterize here. We not only show that this mapping is invertible but also construct the adequate inversion operation. As an application of this stochastic mapping, we revisit the problem posed to Tsallis practitioners by the zeroth law of thermodynamics, that has bedeviled them for 15 years. To cite this article: C. Vignat, A. Plastino, C. R. Physique 7 (2006).