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Asymptotic results for silent elimination

Abstract : Following the model of Bondesson, Nilsson, and Wikstrand, we consider randomly filled urns, where the probability of falling into urn i is the geometric probability (1-q)qi-1. Assuming n independent random entries, and a fixed parameter k, the interest is in the following parameters: Let T be the smallest index, such that urn T is non-empty, but the following k are empty, then: XT= number of balls in urn T, ST= number of balls in urns with index larger than T, and finally T itself..
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Guy Louchard, Helmut Prodinger. Asymptotic results for silent elimination. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2010, special issue in honor of Laci Babai's 60th birthday: Combinatorics, Groups, Algorithms, and Complexity, Vol. 12 no. 2 (2), pp.185-196. ⟨10.46298/dmtcs.527⟩. ⟨hal-00994591⟩

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