Random Walk Approach to Simple Evolution Model

Abstract

The dynamics of the avalanche width in the evolution model is described using a random walk picture. In this approach the critical exponents for avalanche distribution, $\tau$, and avalanche average time, $\gamma$, are found to be the same as in the previous mean field approximation but SOC appear at ${\lambda }_{critical}=2/3$, which is very close to numerical value. A continuous time random walk is studied numerically as a possible way to reconstruct in simpler concepts the evolution model.

Revised version, a computational mistake eliminated, more explanation added, 16 pages, ReVTeX file