Random Walk Approach to Simple Evolution Model

1995/11/20 by L. Anton, Anton, L.
Mathematics · Physics and Astronomy · #Condensed Matter (cond-mat) #FOS: Physical sciences #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.cond-mat/9511091

openalex publication_date 1995/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Avalanche size distribution in a random walk model
• A new hierarchy of avalanches observed in Bak-Sneppen evolution model
• The avalanche dynamics in Bak-Sneppen evolution model observed with standard distribution width of fitness
• Avalanches in Critical Activated Random Walks
• A universal route from avalanches in mean-field models with random fields to stochastic Poisson branching events