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  • Bulletin of the Australian Mathematical Society, Volume 80, Issue 3
  • December 2009, pp. 353-359

THE AVERAGE DISTANCE BETWEEN TWO POINTS

  • BERNHARD BURGSTALLER (a1) and FRIEDRICH PILLICHSHAMMER (a2)
  • DOI: http://dx.doi.org/10.1017/S0004972709000707
  • Published online: 01 October 2009
Abstract
Abstract

We provide bounds on the average distance between two points uniformly and independently chosen from a compact convex subset of the s-dimensional Euclidean space.

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Copyright
Corresponding author
For correspondence; e-mail: friedrich.pillichshammer@jku.at
Linked references
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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1]V. S. Alagar , ‘The distribution of the distance between random points’, J. Appl. Probab. 13 (1976), 558566.

[2]R. S. Anderssen , R. P. Brent , D. J. Daley and P. A. P. Moran , ‘Concerning ∫ 10⋯∫ 10(x21+⋯+x2k)1/2 dx1⋯ dxk and a Taylor series method’, SIAM J. Appl. Math. 30 (1976), 2230.

[4]S. R. Dunbar , ‘The average distance between points in geometric figures’, College Math. J. 28 (1997), 187197.

[5]D. J. Gates , ‘Asymptotics of two integrals from optimization theory and geometric probability’, Adv. Appl. Probab. 17 (1985), 908910.

[6]P. Nickolas and D. Yost , ‘The average distance property for subsets of Euclidean space’, Arch. Math. (Basel) 50 (1988), 380384.

[7]F. Pillichshammer , ‘A note on the sum of distances under a diameter constraint’, Arch. Math. (Basel) 77 (2001), 195199.

[9]H. Solomon , Geometric Probability, CBMS-NSF Regional Conference Series in Applied Mathematics, 28 (SIAM, Philadelphia, PA, 1978).

[10]R. Wolf , ‘On the average distance property and certain energy integrals’, Ark. Mat. 35 (1997), 387400.

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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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