Random circles in the d-dimensional unit ball

Random circles in the d-dimensional unit ball

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Article ID: iaor1990503
Country: Israel
Volume: 26
Issue: 2
Start Page Number: 89
End Page Number: 102
Publication Date: Jun 1989
Journal: Journal of Applied Probability
Authors:
Abstract:

This note gives the solution of the following problem concerning geometric probabilities. What is the probability equ1that the circumference determined by three points P, equ2 and equ3chosen independently and uniformly at random in the interior of a d-dimensional unit ball equ4in Euclidean space equ5is entirely contained in equ6From our results we conclude that equ7ad equ8.

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