Poisson convergence in the restricted $k$-partioning problem
<|reference_start|>Poisson convergence in the restricted $k$-partioning problem: 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.<|reference_end|>
@article{bovier2004poisson,
    title={Poisson convergence in the restricted $k$-partioning problem},
    author={Anton Bovier (WIAS-Berlin, TU-Berlin), Irina Kurkova (U Paris 6)},
    journal={arXiv preprint arXiv:cond-mat/0409532},
    year={2004},
    number={WIAS-preprint 964},
    archivePrefix={arXiv},
    eprint={cond-mat/0409532},
    primaryClass={cond-mat.dis-nn cs.CC math.PR}
}