Covering Random Points in a Unit Disk
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چکیده
Let D be the punctured unit disk. It is easy to see that no pair x, y in D can cover D in the sense that D cannot be contained in the union of the unit disks centred at x and y. With this fact in mind, let Vn = {X1, X2, . . . , Xn}, where X1, X2, . . . are random points sampled independently from a uniform distribution on D. We prove that, with asymptotic probability one, there are two points in Vn that cover all of Vn.
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تاریخ انتشار 2007