Dresden 2006 – wissenschaftliches Programm

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AKSOE: Physik sozio-ökonomischer Systeme

AKSOE 10: Poster Session (posters are expected to be displayed the full day 8:30-18:00)

AKSOE 10.67: Poster

Mittwoch, 29. März 2006, 16:00–18:00, P2

An analytical solution of a wealth exchange model — •Przemyslaw Repetowicz and Peter Richmond — Department of Physics, Trinity College Dublin 2

We solve analyticaly a toy version of a Boltzmann model with applications in economics. This model was first proposed by [1,2] and analysed numericaly in [3,4,5]. The authors studied variants of the model and claimed that in one case the steady state corresponds to a Gamma function [3,4] and in another case that it corresponds to a distribution with a power law with index unity [5] in the high end.It was suggested that the existence of equillibria and the power law exponent of unity are universal features of the model. More recent [6,7] analytical calculations revealed that the Gamma function is only a approximation to a steady state solution.In this work we analyze the existence of equillibrium and the rate of convergence to it. Our approach rest on a body of other work published many years ago [8] and more recently studies using probabilistic tools [9,10].

[1] Chatterjee A et al, Physica Scripta T 106, p 36-38 (2003) and cond-mat/0311227

[2] Chatterjee A et al, Physica A 335 155–163 (2004)

[3] Patriarca M et al, preprint cond-mat/0312167

[4] Patriarca M et al, preprint cond-mat/0402200

[5] Patriarca M et al, preprint cond-mat/0504153

[6] Repetowicz P et al, Physica A, 356 (2005) 641-654

[7] Chatterjee A et al, preprint cond-mat/0407770

[8] Wild E, Proc. Camb Phil Soc 47 (1951) 602-609

[9] Ferland R et al, Stochastics Rep. 35 (1991) 23-33

[10] Carlen E A et al, Jour. Func. Analysis