Theorem: BTW tail integral int_1^inf 2/sqrt(s) ds = inf (Borel-Cantelli infinite-avalanche criterion)

Theorem (BTW tail-divergence via Borel-Cantelli canonical): for the BTW-universality avalanche-size exponent tau = 3/2, the tail probability P(S > s_0) = integral_{s_0}^infinity s^(-3/2) ds = 2/sqrt(s_0). The integral of this tail over s_0…