Divergence rates for the number of rare numbers |
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Authors: | Eric S. Key |
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Affiliation: | (1) Department of Mathematical Sciences, University of Wisconsin-Milwaukee, 53201 Milwaukee, Wisconsin |
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Abstract: | Suppose thatX1,X2, ... is a sequence of i.i.d. random variables taking value inZ+. Consider the random sequenceA(X)(X1,X2,...). LetYn be the number of integers which appear exactly once in the firstn terms ofA(X). We investigate the limit behavior ofYn/E[Yn] and establish conditions under which we have almost sure convergence to 1. We also find conditions under which we dtermine the rate of growth ofE[Yn]. These results extend earlier work by the author. |
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Keywords: | Rare numbers almost sure convergence subadditive |
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