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

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## Abstract

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## 1. Introduction

## 2. The Classical CLT Formulation

## 3. CLT for a Population of Gaussian Random Variables

## 4. Application of the CLT in the HEBP

## 5. Discussions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

MDPI | Multidisciplinary Digital Publishing Institute |

CLT | Central Limit Theorem |

MSD | Mean squared displacement |

VACF | Velocity auto-correlation function |

Bm | Brownian motion |

HEPB | Heterogeneous ensemble of Brownian particles |

Probability density function |

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**MDPI and ACS Style**

Vitali, S.; Budimir, I.; Runfola, C.; Castellani, G. The Role of the Central Limit Theorem in the Heterogeneous Ensemble of Brownian Particles Approach. *Mathematics* **2019**, *7*, 1145.
https://doi.org/10.3390/math7121145

**AMA Style**

Vitali S, Budimir I, Runfola C, Castellani G. The Role of the Central Limit Theorem in the Heterogeneous Ensemble of Brownian Particles Approach. *Mathematics*. 2019; 7(12):1145.
https://doi.org/10.3390/math7121145

**Chicago/Turabian Style**

Vitali, Silvia, Iva Budimir, Claudio Runfola, and Gastone Castellani. 2019. "The Role of the Central Limit Theorem in the Heterogeneous Ensemble of Brownian Particles Approach" *Mathematics* 7, no. 12: 1145.
https://doi.org/10.3390/math7121145