~ Avalanche(a,b)
Avalanches are a common process, occuring anywhere that a system can store stress temporarily without “snapping”. It can happen on sand dunes and solar flares as easily as on the snow bound Alps.
Melatos, Peralta, & Wyithe (arXiv:0710.1021) have a nice summary of avalanche processes in the context of pulsar glitches. Their primary purpose is to show that the glitches are indeed consistent with an avalanche, and along the way they give a highly readable description of what an avalanche is and what it entails. Briefly, avalanches result in event parameters that are distributed in scale invariant fashion (read: power laws) with exponential waiting time distributions (i.e., Poisson).
Hence the title of this post: the “Avalanche distribution” (indulge me! I’m using stats notation to bury complications!) can be thought to have two parameters, both describing the indices of power-law distributions that control the event sizes, a, and the event durations, b, and where the event separations are distributed as an exponential decay. Is there a canned statistical distribution that describes all this already? (In our work modeling stellar flares, we assumed that b=0 and found that a>2 a<-2, which has all sorts of nice consequences for coronal heating processes.)