Université Paris 6
Pierre et Marie Curie | Université Paris 7
Denis Diderot | |

CNRS U.M.R. 7599
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``Probabilités et Modèles Aléatoires''
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**Auteur(s): **

**Code(s) de Classification MSC:**

- 60K40 Other physical applications of random processes
- 60B12 Limit theorems for vector-valued random variables (infinite-dimensional case)

**Résumé:** 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.

**Mots Clés:** *Number partioning ; extreme values ; Poisson process ; Random Energy Model *

**Date:** 2004-09-24

**Prépublication numéro:** *PMA-935*