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Power-law exponent of the Bouchaud-M\'ezard model on regular random network


  • Takashi Ichinomiya


We study the Bouchaud-M\'ezard model on a regular random network. By assuming adiabaticity and independency, and utilizing the generalized central limit theorem and the Tauberian theorem, we derive an equation that determines the exponent of the probability distribution function of the wealth as $x\rightarrow \infty$. The analysis shows that the exponent can be smaller than 2, while a mean-field analysis always gives the exponent as being larger than 2. The results of our analysis are shown to be good agreement with those of the numerical simulations.

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  • Takashi Ichinomiya, 2013. "Power-law exponent of the Bouchaud-M\'ezard model on regular random network," Papers 1307.4821,
  • Handle: RePEc:arx:papers:1307.4821

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    1. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-651, October.
    2. Bruno Bouchard & Marcel Nutz, 2013. "Arbitrage and duality in nondominated discrete-time models," Papers 1305.6008,, revised Mar 2015.
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