Avalanche size distribution in a random walk model

TL;DR

This paper presents a simple one-dimensional model for avalanche size distribution using a directed random walk, capturing key features of self-organized critical phenomena like earthquakes.

Contribution

It introduces a novel random walk-based model that reproduces scaling laws and size distribution exponents observed in avalanches and earthquakes.

Findings

Derives a size distribution law with an exponent of 4/3.

Establishes scaling laws relating avalanche frequency, size, and width.

Models qualitative features of self-organized critical systems.

Abstract

We introduce a simple model for the size distribution of avalanches based on the idea that the front of an avalanche can be described by a directed random walk. The model captures some of the qualitative features of earthquakes, avalanches and other self-organized critical phenomena in one dimension. We find scaling laws relating the frequency, size and width of avalanches and an exponent $4/3$ in the size distribution law.