Quermass-interaction process with convex compact grains

Abstrakt

The paper concerns an extension of random disc Quermass-interaction process, i.e. the model of discs with mutual interactions, to the process of interacting objects of more general shapes. Based on the results for the random disc process and the process with polygonal grains, theoretical results for the generalized process are derived.

Further, a simulation method, its advantages and the corresponding complications are described, and some examples are introduced. Finally, a short comparison to the random disc process is given.

Klíčová slova

• attractiveness
• germ-grain model
• Markov Chain Monte Carlo simulation
• Quermass-interaction process
• random set
• repulsiveness
• Ruelle stability