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We study the statistics of stresses at the grain scale in the context of a lattice model with gravity. The model samples all vector force balanced configurations on the lattice with equal weight. We solve for the probability distribution of local pressures and confirm our results with Monte Carlo simulations. The probability of large stresses decays as a Gaussian, in qualitative difference from earlier lattice models that incorporate scalar force balance and∕or a different statistical sampling of the configuration space.
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