PACKING DENSITIES AND SIMULATED TEMPERING FOR HARD CORE GIBBS POINT PROCESSES

S. MASE^{1}, J. MØLLER^{2}, D. STOYAN^{3}, R. P. WAAGEPETERSEN^{2}, G. DÖGE^{3}

1Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Oh-Okayama, 2-12-1, Meguro-ku, Tokyo 152-8552, Japan 2Department of Mathematical Sciences, Aalborg University, Fredrik Bajers Vej 7E, DK-9220 Aalborg Ø, Denmark 3Institute of Stochastics, Bergakademie Freiberg, Bernhard-von-Cotta-Str. 2, D-09596 Freiberg, Germany

(Received April 1, 1999; revised September 4, 2000)

Abstract. Monotonicity and convergence properties of the intensity of hard core Gibbs point processes are investigated and compared to the closest packing density. For such processes simulated tempering is shown to be an efficient alternative to commonly used Markov chain Monte Carlo algorithms. Various spatial characteristics of the pure hard core process are studied based on samples obtained with the simulated tempering algorithm.

Key words and phrases: Closest packing density, hard core Gibbs point processes, intensity, Markov chain Monte Carlo, Metropolis-Hastings, phase transition, simulated tempering, spatial statistics, statistical physics, stochastic geometry.