A hard core process (HCP) deals with the deposition of hard spheres, generally of the same radius, that are forbidden to overlap. Suppose instead that the identical spheres are replaced with distinct shapes, e.g. spheres of distinct radii, or cuboids of distinct dimensions that can deposit in different orientations.

Is the resulting process a valid example of a marked HCP?

  • When nonidentical spheres attach, the marks are their radii.
  • When cuboids attach, the marks are their dimensions and orientation at the time of deposit.
  • $\begingroup$ Boy, this sure looks like homework. Have you looked at the "help" recommendations for presenting and labeling "self-study" questions? stats.stackexchange.com/questions/tagged/self-study I think such question that include learners efforts will provides more properly targeted responses. $\endgroup$ – DWin Sep 30 '16 at 18:41
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    $\begingroup$ Ok, it's not homework, and I'm not a student either. $\endgroup$ – PKG Sep 30 '16 at 19:07
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    $\begingroup$ This doesn't look like self-study at all: it looks like a genuine question. But in what sense do you define "marked"? In its standard sense the point process should be a relatively "simple" process when you ignore the marking, but in your case--depending on how these "attachments" are assumed to arise--it sure looks like the changes in geometry and orientation could profoundly affect the point process that describes the object centers. In that sense it doesn't look terribly useful to try to describe or analyze it as "marked." $\endgroup$ – whuber Sep 30 '16 at 19:20

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