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Number of survivors in the presence of a demon

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Abstract

This paper complements the analysis of Louchard and Prodinger [LP08] on the number of rounds in a coin-flipping selection algorithm that occurs in the presence of a demon. We precisely analyze a very different aspect of the selection algorithm, using different methods of analysis. Specifically, we obtain precise descriptions of the distribution and all moments of the number of participants ultimately selected during the execution of the algorithm. The selection algorithm is robust in at least two significant ways. The presence of a demon allows for the precise analysis even when errors may occur between the rounds of the selection process. (The analysis also handles the more traditional case, in which no demon is involved.) The selection algorithm can also use either biased or unbiased coins.

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Authors and Affiliations

  1. Département d’Informatique, Université Libre de Bruxelles, CP 212, Boulevard du Triomphe, B-1050, Bruxelles, Belgium

    Guy Louchard

  2. Department of Mathematics, University of Stellenbosch, 7602, Stellenbosch, South Africa

    Helmut Prodinger

  3. Department of Statistics, Purdue University, 150 North University St., West Lafayette, IN, 47907-2067, USA

    Mark Daniel Ward

Authors
  1. Guy Louchard
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  2. Helmut Prodinger
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  3. Mark Daniel Ward
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Corresponding author

Correspondence to Guy Louchard.

Additional information

Communicated by Bálint Tóth

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Louchard, G., Prodinger, H. & Ward, M.D. Number of survivors in the presence of a demon. Period Math Hung 64, 101–117 (2012). https://doi.org/10.1007/s10998-012-9101-9

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  • DOI: https://doi.org/10.1007/s10998-012-9101-9

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