PMID: 15244892Jul 13, 2004Paper

Biased growth processes and the "rich-get-richer" principle

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Alessandro P S de Moura

Abstract

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.

References

Oct 16, 1999·Science·A L Barabasi, R Albert
Oct 18, 2000·Nature·H JeongA L Barabási
Nov 18, 2000·Physical Review Letters·P L KrapivskyF Leyvraz
Jun 21, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·P L Krapivsky, S Redner
Sep 26, 2001·Proceedings. Biological Sciences·R V Solé, J M Montoya
Aug 22, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Adilson E MotterPartha Dasgupta

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Citations

Aug 30, 2008·International Journal of Health Geographics·Beatrix Groneberg-KloftCristian Scutaru

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