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Rare numbers
Authors:Eric S. Key
Affiliation:(1) Department of Mathematical Sciences, University of Wisconsin-Milwaukee, 53201 Milwaukee, Wisconsin
Abstract:Suppose thatX1,X2,... is a sequence of iid random variables taking values inZ+. Consider the random sequenceA(X)equiv(X1,X2,...). LetYn be the number of integers which appear exactly once in the firstn terms ofA(X). We investigate the limit behavior ofn–(1–delta)Yn for deltaepsiv[0, 1].
Keywords:Random sequences  almost sure convergence  summability
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