Sampling rare fluctuations of height in the Oslo ricepile model

TL;DR

This paper investigates the probability of rare large deviations in the height of the Oslo ricepile model using advanced Monte Carlo simulations, confirming a specific exponential decay pattern for large negative fluctuations.

Contribution

It provides the first numerical verification of the predicted large deviation form for height fluctuations in the Oslo ricepile model.

Findings

Confirmed the exponential decay form of large negative height fluctuations.

Achieved sampling of probabilities as low as 10^{-100}.

Validated the theoretical prediction of the fluctuation probability distribution.

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 $\Delta h=-\alpha L$ about the mean varies as $\exp(-\kappa {\alpha}^4 L^3)$ as $L \to \infty$ with $\alpha $ held fixed, and $\kappa > 0$.