Sampling rare fluctuations of height in the Oslo ricepile model

Abstract

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 $Δh=-αL$ about the mean varies as $\exp(-κα^4 L^3)$ as $L \to \infty$ with $α$ held fixed, and $κ> 0$.