Results on the contact process with dynamic edges or under renewals

TL;DR

This paper investigates variants of the contact process with dynamic edges and renewal mechanisms, providing a renormalization approach to analyze their phase diagrams and extinction properties.

Contribution

It introduces a robust renormalization method to study contact process variants with dynamic structures and extends results to new models with dynamic edges and renewal features.

Findings

Established conditions for extinction in models with dynamic edges.

Analyzed phase diagrams of the contact process with renewals.

Developed a general renormalization framework for these models.

Abstract

We analyze variants of the contact process that are built by modifying the percolative structure given by the graphical construction and develop a robust renormalization argument for proving extinction in such models. With this method, we obtain results on the phase diagram of two models: the Contact Process on Dynamic Edges introduced by Linker and Remenik and a generalization of the Renewal Contact Process introduced by Fontes, Marchetti, Mountford and Vares.