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Markov chain analysis of an agent based growth model

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Abstract

In this paper we investigate the asymptotic behavior of a discrete and probabilistic dynamical system which can be described as a growth model where autonomous agents aggregates. The aim of this paper is to give a mathematical analysis of the dynamics. The analysis uses face homogeneous Markov chains and thanks to this study we validate a conjecture set by Laszlo Gulyas and Yuri Mansury concerning a growth model for cities where simulations had shown that the sizes of the cities asymptotically distribute as a Zipf's law. In light of our analysis, we discuss how the emergence of such a Zipf's law could be expected in Gulyas-Mansury' model and in its variants.
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Dates and versions

ensl-00139268 , version 1 (30-03-2007)

Identifiers

  • HAL Id : ensl-00139268 , version 1

Cite

Eric Thierry, Bruno Gaujal, Laszlo Gulyas, Yuri Mansury. Markov chain analysis of an agent based growth model. 2007. ⟨ensl-00139268⟩
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