Probability distribution of residence-times of grains in sandpile models

Abstract

We show that the probability distribution of the residence-times of sand grains in sandpile models, in the scaling limit, can be expressed in terms of the survival probability of a single diffusing particle in a medium with absorbing boundaries and space-dependent jump rates. The scaling function for the probability distribution of residence times is non-universal, and depends on the probability distribution according to which grains are added at different sites. We determine this function exactly for the 1-dimensional sandpile when grains are added randomly only at the ends. For sandpiles with grains are added everywhere with equal probability, in any dimension and of arbitrary shape, we prove that, in the scaling limit, the probability that the residence time greater than t is exp(-t/M), where M is the average mass of the pile in the steady state. We also study finite-size corrections to this function.

arXiv comment8 pages, 5 figures, extra file deleted

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Cited by in corpus (5)

• Diffusion in stochastic sandpiles
• Density relaxation in conserved Manna sandpiles
• Hydrodynamics, density fluctuations and universality in conserved stochastic sandpiles
• Activity, diffusion, and correlations in a two-dimensional conserved stochastic sandpile
• Generic power laws in higher-dimensional lattice models with multidirectional hopping