Poisson convergence in the restricted k-partitioning problem
Please always quote using this URN:urn:nbn:de:0296-matheon-1620
- 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.
Author: | Anton Bovier, Irina Kurkova |
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URN: | urn:nbn:de:0296-matheon-1620 |
Referee: | Günter M. Ziegler |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2004/09/20 |
Release Date: | 2004/09/20 |
Institute: | Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS) |
Preprint Number: | 156 |