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The random volume of interpenetrating spheres in space
P. A. P. Moran
Journal:

Journal of Applied Probability / Volume 10 / Issue 2 / June 1973

Published online by Cambridge University Press:

14 July 2016, pp. 483-490

Print publication:

June 1973
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The distribution of the volume occupied by random spheres in a cube is considered, both when the number of spheres is fixed and when their centres form a Poisson field. The mean and variance are obtained and in the latter case the distribution is proved to converge to normality. The probability of complete coverage is also obtained heuristically.

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The random volume of interpenetrating spheres in space