# A 2-spine Decomposition of the Critical Galton-Watson Tree and a Probabilistic Proof of Yaglom's Theorem

## TL;DR

This paper introduces a two-spine decomposition method for critical Galton-Watson trees and employs it to provide a probabilistic proof of Yaglom's theorem, enhancing understanding of branching processes.

## Contribution

It presents a novel two-spine decomposition technique and offers a probabilistic proof of Yaglom's theorem, advancing theoretical tools in branching process analysis.

## Key findings

- Two-spine decomposition of critical Galton-Watson trees
- Probabilistic proof of Yaglom's theorem
- Enhanced understanding of branching process behavior

## Abstract

In this note we propose a two-spine decomposition of the critical Galton-Watson tree and use this decomposition to give a probabilistic proof of Yaglom's theorem.