Mean field frozen percolation

TL;DR

This paper introduces a mean field frozen percolation model based on a modified Erdos-Renyi process, analyzing its behavior through differential equations to reveal self-organized criticality and extremum properties.

Contribution

It presents a novel mean field frozen percolation process and analyzes its properties using differential equations, including limit theorems for component sizes.

Findings

Demonstrates self-organized criticality in the model

Establishes extremum properties of the process

Proves limit theorems for component size distribution

Abstract

We define a modification of the Erdos-Renyi random graph process which can be regarded as the mean field frozen percolation process. We describe the behavior of the process using differential equations and investigate their solutions in order to show the self-organized critical and extremum properties of the critical frozen percolation model. We prove two limit theorems about the distribution of the size of the component of a typical frozen vertex.