Random walks, Avalanches and branching processes

TL;DR

This paper explores the fundamental connections between Bernoulli random walks, avalanche models, and branching processes, revealing their underlying equivalence to provide new insights into their properties.

Contribution

It demonstrates the essential identity among these models, offering alternative perspectives and deeper understanding of their behaviors.

Findings

Bernoulli random walks, avalanche models, and branching processes are fundamentally equivalent.

The identity provides new analytical insights into the properties of these models.

This equivalence can simplify the analysis of complex stochastic systems.

Abstract

Bernoulli random walks, a simple avalanche model, and a special branching process are essesntially identical. The identity gives alternative insights into the properties of these basic model sytems.