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Is there a rigorous proof that the abelian sandpile model generates a power law distribution of avalanche lengths?

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    $\begingroup$ I saw an interesting review article pop up on the arXiv today. One of the interesting statements it makes is "Over the years, it became increasingly clear that the sandpile model has some rather unfortunate features, in particular, that its supposed scaling behavior could never be fully determined" (Watkins and others arXiv:1504.04991). It gives some references, and might be a good place to start looking. $\endgroup$ – Yoav Kallus Apr 22 '15 at 0:09
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A recent paper http://arxiv.org/abs/1602.06475 claims a proof of lower estimates for the sizes of toppling clusters.

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  • $\begingroup$ How related are 1/f noise and self-organized criticality? And separately. Does sandpile model exhibit 1/f noise of any kind? $\endgroup$ – john mangual Apr 2 '16 at 18:25
  • $\begingroup$ As far as I understand this, 1/f-noise is the same as power-law distributions conceptually, so "yes", it is rather the question of terminology. Probably, a physicists' point of view is different. $\endgroup$ – Nikita Kalinin Apr 4 '16 at 1:13
  • $\begingroup$ As far as I understand, this would however still not prove a power law distribution...just that it is lower bounded by a power law... $\endgroup$ – Engineer trying math Oct 11 at 6:20

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