Vol. 5, No. 3, 2012

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Bounds on the artificial phase transition for perfect simulation of hard core Gibbs processes

Mark L. Huber, Elise Villella, Daniel Rozenfeld and Jason Xu

Vol. 5 (2012), No. 3, 247–255

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 depends on 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.

spatial point process, dominated coupling from the past, birth-death chain
Mathematical Subject Classification 2010
Primary: 62M30
Secondary: 60G55, 60K35
Received: 15 October 2010
Revised: 4 January 2012
Accepted: 13 January 2012
Published: 14 April 2013

Communicated by John C. Wierman
Mark L. Huber
Department of Mathematical Sciences
Claremont McKenna College
850 Columbia Avenue
Claremont, CA 91711
United States
Elise Villella
Massachusetts Institute of Technology
320 Memorial Drive
Cambridge, MA 02139
United States
Daniel Rozenfeld
Harvey Mudd College
340 East Foothill Boulevard
Claremont, CA 91711
United States
Jason Xu
University of Arizona
1021 W. Green Pebble Drive
Tucson, AZ 85755
United States