## Abstract

The distribution of wealth in human populations displays a Log-Gauss-Pareto composite statistical structure: its density is Log-Gauss in its central body, and follows power-law decay in its tails. This composite statistical structure is further observed in other complex systems, and on a logarithmic scale it displays a Gauss-Exponential structure: its density is Gauss in its central body, and follows exponential decay in its tails. In this paper we establish an equilibrium Langevin explanation for this statistical phenomenon, and show that: (i) the stationary distributions of Langevin dynamics with sigmoidal force functions display a Gauss-Exponential composite statistical structure; (ii) the stationary distributions of geometric Langevin dynamics with sigmoidal force functions display a Log-Gauss-Pareto composite statistical structure. This equilibrium Langevin explanation is universal - as it is invariant with respect to the specific details of the sigmoidal force functions applied, and as it is invariant with respect to the specific statistics of the underlying noise.

Original language | English (US) |
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Pages (from-to) | 5598-5610 |

Number of pages | 13 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 391 |

Issue number | 22 |

DOIs | |

State | Published - Nov 15 2012 |

## All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Condensed Matter Physics

## Keywords

- ''mild" randomness
- ''wild" randomness
- Exponential tails
- Gauss distribution
- Geometric Langevin dynamics
- Geometric Ornstein-Uhlenbeck dynamics
- Langevin dynamics
- Laplace distribution
- Linear forces
- Log-Gauss distribution
- Log-Laplace distribution
- Ornstein-Uhlenbeck dynamics
- Power-law tails
- Sigmoidal forces
- Universality