Waves in the sandpile model on fractal lattices

The scaling properties of waves of topplings of the sandpile model on a fra ctal lattice are investigated. The exponent describing the asymptotics of t he distribution of last waves in an avalanche is found. Predictions for sca ling exponents in the forward and backward conditional probabilities for tw o consecutive waves are given. All predictions were examined by simulations on the Sierpinski gasket and were found to be in a reasonable agreement wi th the numerical data. (C) 2001 Elsevier Science B.V. All rights reserved.