Sampling rare fluctuations of height in the Oslo ricepile model

Details Sampling rare fluctuations of height in the Oslo ricepile model Sampling rare fluctuations of height in the Oslo ricepile model

2006-08-06

arxiv.org/abs/cond-mat/0608144v1

J. Phys. A: Math. Theor. 40, 2639 (2007).

Physics

Condensed Matter

Statistical Mechanics

7 pages, 8 figures

Scientific paper

10.1088/1751-8113/40/11/003

We have studied large deviations of the height of the pile from its mean value in the Oslo ricepile model. We sampled these very rare events with probabilities of order $10^{-100}$ by Monte Carlo simulations using importance sampling. These simulations check our qualitative arguement [Phys. Rev. E, {\bf 73}, 021303, 2006] that in steady state of the Oslo ricepile model, the probability of large negative height fluctuations $\Delta h=-\alpha L$ about the mean varies as $\exp(-\kappa {\alpha}^4 L^3)$ as $L \to \infty$ with $\alpha $ held fixed, and $\kappa > 0$.

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