# 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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https://hal.archives-ouvertes.fr/hal-00828456
Contributor : Antoine Chevreuil <>
Submitted on : Friday, May 31, 2013 - 9:56:39 AM
Last modification on : Wednesday, April 8, 2020 - 3:51:54 PM
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• HAL Id : hal-00828456, version 1

### Citation

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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