On a conjecture about Diracs delta representation using q-GaussiansReport as inadecuate

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1 LIGM - Laboratoire d-Informatique Gaspard-Monge 2 Depto. de Fisica, Universidad Nacional de La Plata, C.C. 727, 1900 La Plata, Argentina Depto. de Fisica 3 L2S - Laboratoire des signaux et systèmes

Abstract : Tsallis and Jauregui have recently conjectured a representation of the celebrated Dirac delta distribution, which they call $\delta qx$, 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.

Author: Antoine Chevreuil - Angelo Plastino - Christophe Vignat -

Source: https://hal.archives-ouvertes.fr/


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