Poisson convergence in the restricted $k$-partioning problem

Details Poisson convergence in the restricted $k$-partioning problem Poisson convergence in the restricted $k$-partioning problem

2004-09-21

arxiv.org/abs/cond-mat/0409532v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

31pp, AMSTeX

Scientific paper

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.

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