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Sandpiles, Staircases and Self-organized criticality

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In the fixed-energy sandpile model, `activity density’ jumps are observed as the particle density increases, in some cases even seeming to form a devil’s staircase. After presenting new results on this topic, we will focus on the first jump, from zero to nonzero activity density. The particle density where this transition takes place, plays a role in a popular heuristic argument to explain self-organized criticality in sandpile models: it is argued that another, differently defined particle density is in fact the same. This conjecture was supported by simulations and generally believed to be true. However, we can now for several cases exactly calculate both densities, giving very close, but unequal values. (joint work with Lionel Levine and David Wilson)

This talk is part of the Probability series.

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