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Random sequential packing in Euclidean spaces of dimensions three and four and a conjecture of Palásti

Published online by Cambridge University Press:  14 July 2016

B. Edwin Blaisdell  and
Herbert Solomon
B. Edwin Blaisdell*
Affiliation:
Linus Pauling Institute of Science and Medicine
Herbert Solomon*
Affiliation:
Stanford University
*
∗ Postal address: Linus Pauling Institute of Science and Medicine, 440 Page Mill Road, Palo Alto, CA 94306, U.S.A.
∗∗ Postal address: Department of Statistics, Sequoia Hall, Stanford University, Stanford, CA 94305, U.S.A.
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Abstract

A conjecture of Palásti [11] that the limiting packing density β d in a space of dimension d equals β d where ß is the limiting packing density in one dimension continues to be studied, but with inconsistent results. Some recent correspondence in this journal [7], [8], [13], [14], [15], [16], [18], [19], [20] as well as some other papers indicate a lively interest in the subject. In a prior study [3], we demonstrated that the conjectured value in two dimensions was smaller than the actual density. Here we demonstrate that this is also so in three and four dimensions and that the discrepancy increases with dimension.

Keywords

SEQUENTIAL RANDOM PACKINGPALÁSTI CONJECTUREGEOMETRICAL PROBABILITY

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 19 , Issue 2 , June 1982 , pp. 382 - 390
Copyright
Copyright © Applied Probability Trust 1982 

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Footnotes

Partial support by Office of Naval Research Contract No. N00014-76-C-0475, Stanford University.

References

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