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Limit distributions of the number of vectors satisfying a linear relation
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V. I. Kruglov
Published/Copyright:
December 15, 2008
Abstract
Let X1, …, XT be independent random elements uniformly distributed on a finite Abelian group G. In this paper, we give conditions under which the number of ordered sets (i1, …, ik) of pairwise distinct numbers in {1, …, T} such that a1Xi1 + … + akXik = 0 where a1, …, ak are fixed integers has the Poisson limit distribution as T → ∞ and the group G varies with T. We give an example of a sequence of groups G for which the limit distribution of the number of ordered sets is the compound Poisson distribution.
Received: 2007-12-26
Published Online: 2008-12-15
Published in Print: 2008-December
© de Gruyter 2008
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Articles in the same Issue
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- On design of circuits of logarithmic depth for inversion in finite fields
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