Cosmic crystallography in a circle
Abstract
In a circle (an S1) with circumference 1 assume m objects distributed pseudo-randomly. In the universal covering R1 assume the objects replicated accordingly, and take an interval L>1. In this interval, make the normalized histogram of the pair separations which are not an integer. The theoretical (expected) such histogram is obtained in this report, as well as its difference to a similar histogram for non-replicated objects. The whole study is of interest for the cosmic crystallography.
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