Bounds on the artificial phase transition for perfect simulation of repulsive point processes

TL;DR

This paper investigates the artificial phase transition in perfect simulation algorithms for repulsive point processes, providing improved bounds and empirical analysis of the transition point.

Contribution

The paper improves the lower bounds on the artificial phase transition and presents computer experiments to better locate this transition.

Findings

Enhanced lower bounds on the phase transition point.

Empirical results illustrating the transition behavior.

Insights into the algorithm's running time relative to intensity.

Abstract

Repulsive point processes arise in models where competition forces entities to be more spread apart than if placed independently. Simulation of these types of processes can be accomplished using dominated coupling from the past with a running time that varies as the intensity of the number of points. These algorithms usually exhibit what is called an artificial phase transition, where below a critical intensity the algorithm runs in finite expected time, but above the critical intensity the expected number of steps is infinite. Here the artificial phase transition is examined. In particular, an earlier lower bound on this artificial phase transition is improved by including a new type of term in the analysis. In addition, the results of computer experiments to locate the transition are presented.