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About closedness by convolution of the Tsallis maximizers

Author

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  • Vignat, C
  • Hero III, A.O
  • Costa, J.A

Abstract

In this paper, we study the stability under convolution of the maximizing distributions of the Tsallis entropy under energy constraint (called hereafter Tsallis distributions). These distributions are shown to obey three important properties: a stochastic representation property, an orthogonal invariance property and a duality property. As a consequence of these properties, the behavior of Tsallis distributions under convolution is characterized. At last, a special random convolution, called Kingman convolution, is shown to ensure the stability of Tsallis distributions.

Suggested Citation

  • Vignat, C & Hero III, A.O & Costa, J.A, 2004. "About closedness by convolution of the Tsallis maximizers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 340(1), pages 147-152.
    • Handle: RePEc:eee:phsmap:v:340:y:2004:i:1:p:147-152
    DOI: 10.1016/j.physa.2004.04.001
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    Cited by:

    1. Zozor, Steeve & Portesi, Mariela & Vignat, Christophe, 2008. "Some extensions of the uncertainty principle," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(19), pages 4800-4808.
    2. Vignat, C. & Plastino, A., 2006. "Density operators that extremize Tsallis entropy and thermal stability effects," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 361(1), pages 139-160.
    3. Suyari, Hiroki, 2006. "Mathematical structures derived from the q-multinomial coefficient in Tsallis statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 368(1), pages 63-82.
    4. Zozor, S. & Vignat, C., 2007. "On classes of non-Gaussian asymptotic minimizers in entropic uncertainty principles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(2), pages 499-517.

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    Keywords

    Tsallis entropy; Convolution;

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