On a special class of gibbs hard-core point processes modeling random patterns of non-overlapping grains

Abstract

Inspired by issues of formal kinetics in materials science, we consider a class of processes with density with respect to an inhomogeneous finite Poisson point process, which may be regarded as a generalization of the classical Strauss hard-core process. We prove expressions for the intensity measure and the void probabilities, together with upper and lower bounds. A discussion on some special cases of interest, links with literature and a comparison between Matérn I and Strauss hard-core process are also provided. We apply such a special class of point processes in modeling patterns of non-overlapping grains and in the study of the mean volume density of particular birth-and-growth processes.

Keywords:

• Gibbs hard-core point process
• intensity
• germ-grain model
• mean volume density

AMS Classification 2020::

• 60G55
• 60D05

Acknowledgments

The authors would like to thank Harison S. Ventura for the figures, and Professor P.R. Rios of Universidade Federal Fluminense for fruitful discussions on application problems.

EV is member of the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM).

Disclosure statement

The authors report there are no competing interests to declare.