C B Yang 2004 J. Phys. A: Math. Gen. 37 L523 doi:10.1088/0305-4470/37/42/L05
C B Yang
Show affiliationsThe origin of power-law distributions in self-organized criticality is investigated by treating the variation of the number of active sites in the system as a stochastic process. An avalanche is then regarded as a first-return random-walk process in a one-dimensional lattice. Power-law distributions of the lifetime and spatial size are found when the random walk is unbiased with equal probability to move in opposite directions. This shows that power-law distributions in self-organized criticality may be caused by the balance of competitive interactions. At the mean time, the mean spatial size for avalanches with the same lifetime is found to increase in a power law with the lifetime.
05.40.Fb Random walks and Levy flights
82B41 Random walks, random surfaces, lattice animals, etc. (See also 60G50, 82C41)
82C41 Dynamics of random walks, random surfaces, lattice animals, etc. (See also 60G50)
60G20 Generalized stochastic processes
60G50 Sums of independent random variables; random walks
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
Issue 42 (22 October 2004)
Received 4 August 2004, in final form 20 September 2004
Published 6 October 2004
C B Yang 2004 J. Phys. A: Math. Gen. 37 L523
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