Percolation Threshold Results on \Erdos-\Renyi Graphs: an Empirical Process Approach

TL;DR

This paper investigates the percolation threshold in Erdős-Rényi graphs using an empirical process approach, providing weak limit results for the stochastic process involved.

Contribution

It introduces a directed percolation model on Erdős-Rényi graphs and derives weak limit theorems for the associated stochastic process, advancing understanding of percolation phenomena.

Findings

Derived weak limit results for the directed percolation process

Established empirical process framework for Erdős-Rényi graphs

Enhanced theoretical understanding of percolation thresholds

Abstract

In this paper we define a directed percolation over Erdos-Renyi graphs and derive weak limit results for the resulting stochastic process.