Jürgen F Stilck et al 2004 J. Phys. A: Math. Gen. 37 1145 doi:10.1088/0305-4470/37/4/004
Series expansion for a stochastic sandpile
Jürgen F Stilck1, Ronald Dickman2 and Ronaldo R Vidigal2
Show affiliationsUsing operator algebra, we extend the series for the activity density in a one-dimensional stochastic sandpile with fixed particle density p, the first terms of which were obtained via perturbation theory (Dickman and Vidigal 2002 J. Phys. A: Math. Gen. 35 7269). The expansion is in powers of the time; the coefficients are polynomials in p. We devise an algorithm for evaluating expectations of operator products and extend the series to 
. Constructing Padé approximants to a suitably transformed series, we obtain predictions for the activity that compare well against simulations, in the supercritical regime.
- PACS
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05.10.Gg Stochastic analysis methods (Fokker-Planck, Langevin, etc.)
05.50.+q Lattice theory and statistics (Ising, Potts, etc.)
05.70.Fh Phase transitions: general studies
- MSC
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82C22 Interacting particle systems (See also 60K35)
65C35 Stochastic particle methods (See also 82C80)
82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) (See also 60H10)
- Subjects
- Dates
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Issue 4 (30 January 2004)
Received 9 June 2003, in final form 20 October 2003
Published 9 January 2004
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Series expansion for a stochastic sandpile
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