On a conjecture about Dirac's delta representation using q-Gaussians

Abstract : Tsallis and Jauregui have recently conjectured a representation of the celebrated Dirac delta distribution, which they call $\delta_q(x)$, based on $q-$exponential functions. However, they could not prove their conjecture and used numerical experiments that suggest its validity. In this note, we provide a rigourous mathematical approach to this problem and prove their conjecture by recourse to the notion of superstatistics.
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Antoine Chevreuil, Angelo Plastino, Christophe Vignat. On a conjecture about Dirac's delta representation using q-Gaussians. Journal of Mathematical Physics, American Institute of Physics (AIP), 2010, 51 (9), pp.093502. ⟨hal-00828456⟩

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