### Abstract

Original language | English |
---|---|

Article number | 056116 |

Number of pages | 5 |

Journal | Physical Review. E, Statistical, Nonlinear and Soft Matter Physics |

Volume | 69 |

Issue number | 5 pt 2 |

DOIs | |

Publication status | Published - May 2004 |

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**Biased growth and the 'rich-get-richer' principle.** / de Moura, Alessandro Paula Servio.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Biased growth and the 'rich-get-richer' principle

AU - de Moura, Alessandro Paula Servio

PY - 2004/5

Y1 - 2004/5

N2 - We study a simple stochastic system with a "rich-get-richer" behavior, in which there are 2 states, and N particles that are successively assigned to one of the states, with a probability p(i) that depends on the states' occupation n(i) as p(i) = n(gamma)(i)/ n(gamma)(1) + n(gamma)(2)). We show that there is a phase transition as gamma crosses the critical value gamma(c) =1. For gamma<1, in the thermodynamic limit the occupations are approximately the same, n(1) approximately n(2). For gamma>1, however, a spontaneous symmetry breaking occurs, and the system goes to a highly clustered configuration, in which one of the states has almost all the particles. These results also hold for any finite number of states (not only two). We show that this "rich-get-richer" principle governs the growth dynamics in a simple model of gravitational aggregation, and we argue that the same is true in all growth processes mediated by long-range forces like gravity.

AB - We study a simple stochastic system with a "rich-get-richer" behavior, in which there are 2 states, and N particles that are successively assigned to one of the states, with a probability p(i) that depends on the states' occupation n(i) as p(i) = n(gamma)(i)/ n(gamma)(1) + n(gamma)(2)). We show that there is a phase transition as gamma crosses the critical value gamma(c) =1. For gamma<1, in the thermodynamic limit the occupations are approximately the same, n(1) approximately n(2). For gamma>1, however, a spontaneous symmetry breaking occurs, and the system goes to a highly clustered configuration, in which one of the states has almost all the particles. These results also hold for any finite number of states (not only two). We show that this "rich-get-richer" principle governs the growth dynamics in a simple model of gravitational aggregation, and we argue that the same is true in all growth processes mediated by long-range forces like gravity.

U2 - 10.1103/PhysRevE.69.056116

DO - 10.1103/PhysRevE.69.056116

M3 - Article

VL - 69

JO - Physical Review. E, Statistical, Nonlinear and Soft Matter Physics

JF - Physical Review. E, Statistical, Nonlinear and Soft Matter Physics

SN - 1539-3755

IS - 5 pt 2

M1 - 056116

ER -