Equal-time correlation function for directed percolation

TL;DR

This paper introduces a new equal-time n-point correlation function for directed percolation systems, which is well-defined across all phases and independent of initial conditions, providing a robust tool for analyzing such systems.

Contribution

The authors propose a novel equal-time correlation function for directed percolation that remains valid in all phases and does not depend on initial conditions.

Findings

The correlation function is well-defined in all phases.

It is independent of initial conditions.

It connects points via directed paths to a common ancestor.

Abstract

We suggest an equal-time n-point correlation function for systems in the directed percolation universality class which is well defined in all phases and independent of initial conditions. It is defined as the probability that all points are connected with a common ancestor in the past by directed paths.