THE AVERAGE DISTANCE BETWEEN TWO POINTS

DOI10.1017/S0004972709000707zbMath1183.52006MaRDI QIDQ3651078

Bernhard Burgstaller, Friedrich Pillichshammer

Publication date: 8 December 2009

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

uniform distributionaverage distancecompact convex sets

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Integral geometry (53C65) Random convex sets and integral geometry (aspects of convex geometry) (52A22)

Related Items (6)

T-SNE, forceful colorings, and mean field limits ⋮ Continuous approximation formulas for location problems ⋮ Counterintuitive patterns on angles and distances between lattice points in high dimensional hypercubes ⋮ A NOTE CONCERNING THE DISTANCES OF UNIFORMLY DISTRIBUTED POINTS FROM THE CENTRE OF A RECTANGLE ⋮ Limit theorems for additive functionals of stationary fields, under integrability assumptions on the higher order spectral densities ⋮ Sharp inequalities for the mean distance of random points in convex bodies

Cites Work

• The average distance property for subsets of Euclidean space
• On the average distance property and certain energy integrals
• The Average Distance between Points in Geometric Figures
• Asymptotics of two integrals from optimization theory and geometric probability
• Concerning $\int_0^1 \cdots \int_0^1 {(x_1^2 + \cdots + x_k^2 )} ^{{1 / 2}} dx_1 \cdots ,dx_k $ and a Taylor Series Method
• The distribution of the distance between random points
• A note on the sum of distances under a diameter constraint

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