### Abstract

Various clustering properties of d-dimensional overlapping (i.e., Poisson distributed) spheres are investigated. We evaluate n_{k}, the average number of connected clusters of k particles (called k-mers) per unit particle, for k = 2,3,4 and v_{k}, the expected volume of a k-mer, for k = 2,3,4 by using our general expressions for these quantities for d = 1, 2, or 3. We use these calculations to obtain low-density expansions of various averaged cluster numbers and volumes, which can be obtained from the n_{k} and v_{k}. We study the behavior of these cluster statistics as the percolation threshold is approached from below, and we rigorously show that two of these averaged quantities do not diverge for d≥2.

Original language | English (US) |
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Pages (from-to) | 5331-5339 |

Number of pages | 9 |

Journal | Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |

Volume | 54 |

Issue number | 5 |

State | Published - Dec 1 1996 |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics

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## Cite this

*Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*,

*54*(5), 5331-5339.