Coupling from the past for exponentially ergodic one-dimensional probabilistic cellular automata

TL;DR

This paper proves that for one-dimensional exponentially ergodic probabilistic cellular automata with positive rates, a coupling-from-the-past flow with finite exponential coalescence time exists, ensuring rapid convergence to equilibrium.

Contribution

It establishes the existence of a locally defined coupling-from-the-past flow with finite exponential moments for this class of automata, advancing understanding of their ergodic properties.

Findings

Existence of coupling-from-the-past flow with finite exponential coalescence time.

Applicable to all one-dimensional exponentially ergodic probabilistic cellular automata with positive rates.

Provides a method for perfect sampling in this context.

Abstract

We prove that, for every one-dimendional exponentially ergodic probabilistic cellular automaton with positive rates, there exists a locally defined coupling-from-the-past flow whose coalescence time has a finite exponential moment.