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, $τ$, and avalanche average time, $γ$, are found to be the same as in the previous mean field approximation but SOC appear at $λ_{critical}=2/3$, 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.