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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
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Abstract |
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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. |
Keywords
spatial point process, dominated coupling from the past,
birth-death chain
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Mathematical Subject Classification 2010
Primary: 62M30
Secondary: 60G55, 60K35
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Milestones
Received: 15 October 2010
Revised: 4 January 2012
Accepted: 13 January 2012
Published: 14 April 2013
Communicated by John C. Wierman
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Authors |
| Mark L. Huber | |
| Department of Mathematical
Sciences Claremont McKenna College 850 Columbia Avenue Claremont, CA 91711 United States |
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| Elise Villella | |
| Massachusetts Institute of
Technology 320 Memorial Drive Cambridge, MA 02139 United States |
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| Daniel Rozenfeld | |
| Harvey Mudd College 340 East Foothill Boulevard Claremont, CA 91711 United States |
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| Jason Xu | |
| University of Arizona 1021 W. Green Pebble Drive Tucson, AZ 85755 United States |
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