Inversion Symmetry and Critical Exponents of Dissipating Waves in the Sandpile Model

Abstract

Statistics of waves of topplings in the Sandpile model is analysed both analytically and numerically. It is shown that the probability distribution of dissipating waves of topplings that touch the boundary of the system obeys power-law with critical exponent 5/8. This exponent is not indeendent and is related to the well-known exponent of the probability distribution of last waves of topplings by exact inversion symmetry s -> 1/s.