Regeneration of extremal particles for one-dimensional contact processes

TL;DR

This paper introduces a new, elementary proof method for establishing the existence of regenerative points in one-dimensional contact processes, using symmetry and coupling arguments to simplify previous approaches.

Contribution

It provides a novel, simpler proof technique for regenerative points in contact processes, avoiding complex block constructions.

Findings

Existence of regenerative space-time points established

Elementary proof complements previous methods

Uses symmetry-based coupling and convergence to equilibrium

Abstract

A new, conceptual proof approach for establishing the existence of regenerative space-time points for symmetric, translation invariant, finite-range interaction contact processes on survival is shown. The proof is elementary, complements the original one, and employs symmetry-based coupling arguments and a new consequence of convergence to equilibrium of the process in order to circumvent the original block construction.