Abstract
Many complex systems are characterized by power-law distributions, beginning with the first historical example of the Pareto law for the wealth distribution in economic systems. In the case of the Pareto law and other instances of power-law distributions, the power-law tail can be explained in the framework of canonical statistical mechanics as a statistical mixture of canonical equilibrium probability densities of heterogeneous subsystems at equilibrium. In this picture, each subsystem interacts (weakly) with the others and is characterized at equilibrium by a canonical distribution, but the distribution associated to the whole set of interacting subsystems can in principle be very different. This phenomenon, which is an example of the possible constructive role of the interplay between heterogeneity and noise, was observed in numerical experiments of Kinetic Exchange Models and presented in the conference “Econophys-Kolkata-I”, hold in Kolkata in 2005. The 2015 edition, taking place ten years later and coinciding with the twentieth anniversary of the 1995 conference hold in Kolkata where the term “Econophysics” was introduced, represents an opportunity for an overview in a historical perspective of this mechanism within the framework of heterogeneous kinetic exchange models (see also Kinetic exchange models as D-dimensional systems in this volume). We also propose a generalized framework, in which both quenched heterogeneity and time dependent parameters can comply constructively leading the system toward a more robust and extended power-law distribution.
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References
M. Abramowitz and I. A. Stegun, editors. Handbook of Mathematical Functions. Dover, N.Y., 1970.
J. Angle. The surplus theory of social stratification and the size distribution of personal wealth. In Proceedings of the American Social Statistical Association, Social Statistics Section, pages 395–400, Alexandria, VA, 1983.
J. Angle. The surplus theory of social stratification and the size distribution of personal wealth. Social Forces, 65:293–326, 1986.
C. Beck. Stretched exponentials from superstatistics. Physica (Amsterdam), 365A:96, 2006.
C. Beck. Superstatistics in high-energy physics. Eur. Phys. J. A, 40:267–273, 2009.
C. Beck and E.G.D. Cohen. Superstatistics. Physica A, 322:267–275, 2003.
E. Bennati. La simulazione statistica nell’analisi della distribuzione del reddito: modelli realistici e metodo di Monte Carlo. ETS Editrice, Pisa, 1988a.
E. Bennati. Un metodo di simulazione statistica nell’analisi della distribuzione del reddito. Rivista Internazionale di Scienze Economiche e Commerciali, 35:735, August 1988b.
E. Bennati. Il metodo Monte Carlo nell’analisi economica. Rassegna di lavori dell’ISCO, X:31, 1993.
K. Bhattacharya, G. Mukherjee, and S. S. Manna. Detailed simulation results for some wealth distribution models in econophysics. In A. Chatterjee, S.Yarlagadda, and B. K. Chakrabarti, editors, Econophysics of Wealth Distributions, page 111. Springer, 2005.
Anindya S. Chakrabarti and Bikas K. Chakrabarti. Microeconomics of the ideal gas like market models. Physica A, 388:4151–4158, 2009.
A. Chakraborti and B. K. Chakrabarti. Statistical mechanics of money: How saving propensity affects its distribution. Eur. Phys. J. B, 17:167–170, 2000.
A. Chakraborti and M. Patriarca. Gamma-distribution and Wealth inequality. Pramana J. Phys., 71:233, 2008.
A. Chakraborti and M. Patriarca. Variational principle for the Pareto power law. Phys. Rev. Lett., 103:228701, 2009.
A. Chatterjee, B. K. Chakrabarti, and S. S. Manna. Pareto law in a kinetic model of market with random saving propensity. Physica A, 335:155, 2004.
A. Chatterjee and B.K. Chakrabarti. Ideal-Gas Like Markets: Effect of Savings. In A. Chatterjee, S.Yarlagadda, and B. K. Chakrabarti, editors, Econophysics of Wealth Distributions, pages 79–92. Springer, 2005.
A. Chatterjee, S. Yarlagadda, and B. K. Chakrabarti, editors. Econophysics of Wealth Distributions - Econophys-Kolkata I. Springer, 2005.
A. Dragulescu and V. M. Yakovenko. Statistical mechanics of money. Eur. Phys. J. B, 17:723–729, 2000.
W. Feller. volume 1 and 2. John Wiley & Sons, 2nd edition, 1966.
S. Ispolatov, P.L. Krapivsky, S. Redner, Wealth distributions in asset exchange models, Eur. Phys. J. B, 17:723–729, 1998
G. Katriel. Directed Random Market: the equilibrium distribution. Eur. Phys. J. B, 88:19, 2015.
B. Mandelbrot. The Pareto-Levy law and the distribution of income. Int. Econ. Rev., 1:79, 1960.
M. Patriarca and A. Chakraborti. Kinetic exchange models: From molecular physics to social science. Am. J. Phys., 81(8):618–623, 2013.
M. Patriarca, A. Chakraborti, and G. Germano. Influence of saving propensity on the power law tail of wealth distribution. Physica A, 369:723, 2006.
M. Patriarca, A. Chakraborti, E. Heinsalu, and G. Germano. Relaxation in statistical many-agent economy models. Eur. J. Phys. B, 57:219, 2007.
M. Patriarca, A. Chakraborti, and K. Kaski. Gibbs versus non-Gibbs distributions in money dynamics. Physica A, 340:334, 2004a.
M. Patriarca, A. Chakraborti, and K. Kaski. Statistical model with a standard gamma distribution. Phys. Rev. E, 70:016104, 2004b.
M. Patriarca, A. Chakraborti, K. Kaski, and G. Germano. Kinetic theory models for the distribution of wealth: Power law from overlap of exponentials. In A. Chatterjee, S.Yarlagadda, and B. K. Chakrabarti, editors, Econophysics of Wealth Distributions, page 93. Springer, 2005.
M. Patriarca, E. Heinsalu, L. Marzola, A. Chakraborti, and K. Kaski. Power-Laws as Statistical Mixtures, pages 271–282. Springer International Publishing, Switzerland, 2016.
A.C. Silva and V.M. Yakovenko. Temporal evolution of the thermal and superthermal income classes in the USA during 1983-2001. Europhys. Lett., 69:304–310, 2005.
R. A. Treumann and C. H. Jaroschek. Gibbsian Theory of Power-Law Distributions. Phys. Rev. Lett., 100:155005, 2008.
C. Tsallis. Possible generalization of Boltzmann-Gibbs statistics. J. Stat. Phys., 52:479, 1988.
Eric W. Weisstein. Gamma Distribution 2016.
Acknowledgements
M.P. and E.H. acknowledge support from the Institutional Research Funding IUT(IUT39-1) of the Estonian Ministry of Education and Research. A.C. acknowledges financial support from grant number BT/BI/03/004/2003(C) of Government of India, Ministry of Science and Technology, Department of Biotechnology, Bioinformatics Division and University of Potential Excellence-II grant (Project ID-47) of the Jawaharlal Nehru University, New Delhi, India.
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Patriarca, M., Heinsalu, E., Chakraborti, A., Kaski, K. (2017). The Microscopic Origin of the Pareto Law and Other Power-Law Distributions. In: Abergel, F., et al. Econophysics and Sociophysics: Recent Progress and Future Directions. New Economic Windows. Springer, Cham. https://doi.org/10.1007/978-3-319-47705-3_12
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DOI: https://doi.org/10.1007/978-3-319-47705-3_12
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