Bulletin of the Australian Mathematical Society

Research Article

THE AVERAGE DISTANCE BETWEEN TWO POINTS

BERNHARD BURGSTALLERa1 and FRIEDRICH PILLICHSHAMMERa2 c1

a1 Doppler Institute for Mathematical Physics, Trojanova 13, 12000 Prague, Czech Republic (email: bernhardburgstaller@yahoo.de)

a2 Institut für Finanzmathematik, Universität Linz, Altenbergstraße 69, A-4040 Linz, Austria (email: friedrich.pillichshammer@jku.at)

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.

(Received May 19 2008)

2000 Mathematics subject classification

  • primary 52A22; secondary 60D05

Keywords and phrases

  • distance geometry;
  • random convex sets;
  • average distance

Correspondence:

c1 For correspondence; e-mail: friedrich.pillichshammer@jku.at