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Dec 16, 2017 at 23:22 comment added j.c. As I said in my comment to your question (perhaps too obliquely), the estimate 0.82 in the paper you linked is not an estimate of the density of the process you describe in the text of your question. Here's the first line of the abstract of that paper: "A computer simulation study was made of the random packing of unimodal and bimodal circle size distributions under the influence of a weak central force." with italicized emphasis on the part that makes their model different from the one you ask about.
Dec 16, 2017 at 21:30 comment added Wlodek Kuperberg How is the discrepancy explained between the two estimates, 0.547 and 0.82...?
Dec 16, 2017 at 18:51 history answered j.c. CC BY-SA 3.0