Is there a rigorous proof that the abelian sandpile model generates a power law distribution of avalanche lengths?
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asked Mar 16, 2015 at 0:34
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3$\begingroup$ 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 KallusCommented Apr 22, 2015 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.
answered Apr 2, 2016 at 16:08
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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? $\endgroup$ Commented Apr 2, 2016 at 18:25
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$\begingroup$ 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. $\endgroup$ Commented Apr 4, 2016 at 1:13
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$\begingroup$ 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... $\endgroup$ Commented Oct 11, 2019 at 6:20