Stretched exponential decay of correlations in the quasiperiodic continuum percolation model

TL;DR

This paper investigates a continuum percolation model with quasiperiodic disorder, demonstrating that correlations decay in a stretched exponential manner at intermediate disorder strengths, extending understanding of disordered spatial processes.

Contribution

It introduces a continuum percolation model with quasiperiodic disorder and proves stretched exponential decay of correlations, a novel result in this context.

Findings

Correlations decay in a stretched exponential manner.

The decay behavior is established at intermediate disorder strengths.

The model extends percolation theory to quasiperiodic disordered systems.

Abstract

We study the continuum percolation model, which is defined on $\mathbb{Z}^d\times \mathbb{R}$ so that the connections in the continuous directions are not oriented in time, with quasiperiodically disordered fields. The oriented version of the model is the contact process. We consider intermediate strengths of disorder of the fields and show stretched exponential decay of correlations.