Poisson convergence in the restricted k-partitioning problem

  • Authors:

  • Anton Bovier;Irina Kurkova

  • Affiliations:

  • Weierstraß–Institut für Angewandte Analysis und Stochastik, Mohrenstrasse 39, D-10117 Berlin, Germany and Institut für Mathematik, Technische Universität Berlin, Strasse ...;Laboratoire de Probabilités et Modèles Aléatoires, Université Paris 6, 4, place Jussieu, B.C. 188, 75252 Paris, Cedex 5, France

  • Venue:
  • Random Structures & Algorithms
  • Year:
  • 2007

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Abstract

The randomized k-number partitioning problem is the task to distribute N i.i.d. random variables into k groups in such a way that the sums of the variables in each group are as similar as possible. The restricted k-partitioning problem refers to the case where the number of elements in each group is fixed to N/k. In the case k = 2 it has been shown that the properly rescaled differences of the two sums in the close to optimal partitions converge to a Poisson point process, as if they were independent random variables. We generalize this result to the case k 2 in the restricted problem and show that the vector of differences between the k sums converges to a k - 1-dimensional Poisson point process. © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2007