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The Role of the Central Limit Theorem in the Heterogeneous Ensemble of Brownian Particles Approach

Author

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  • Silvia Vitali

    (Department of Physics and Astronomy; University of Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy
    These authors contributed equally to this work.)

  • Iva Budimir

    (Department of Physics and Astronomy; University of Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy
    These authors contributed equally to this work.)

  • Claudio Runfola

    (Department of Physics and Astronomy; University of Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy)

  • Gastone Castellani

    (Department of Physics and Astronomy; University of Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy)

Abstract

The central limit theorem (CLT) and its generalization to stable distributions have been widely described in literature. However, many variations of the theorem have been defined and often their applicability in practical situations is not straightforward. In particular, the applicability of the CLT is essential for a derivation of heterogeneous ensemble of Brownian particles (HEBP). Here, we analyze the role of the CLT within the HEBP approach in more detail and derive the conditions under which the existing theorems are valid.

Suggested Citation

  • Silvia Vitali & Iva Budimir & Claudio Runfola & Gastone Castellani, 2019. "The Role of the Central Limit Theorem in the Heterogeneous Ensemble of Brownian Particles Approach," Mathematics, MDPI, vol. 7(12), pages 1-9, November.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:12:p:1145-:d:290197
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    References listed on IDEAS

    as
    1. Gorenflo, Rudolf & Fabritiis, Gianni De & Mainardi, Francesco, 1999. "Discrete random walk models for symmetric Lévy–Feller diffusion processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 269(1), pages 79-89.
    2. Avelino Javer & Nathan J. Kuwada & Zhicheng Long & Vincenzo G. Benza & Kevin D. Dorfman & Paul A. Wiggins & Pietro Cicuta & Marco Cosentino Lagomarsino, 2014. "Persistent super-diffusive motion of Escherichia coli chromosomal loci," Nature Communications, Nature, vol. 5(1), pages 1-8, September.
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