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# Statistical properties of the Euclidean random assignment problem

Abstract : Given 2n points, n red'' and n blue'', in a Euclidean space,solving the associated Euclidean Assignment Problem consists infinding the bijection between red and blue points that minimizes afunctional of the point positions. In the stochastic version of this problem, the points are a Poisson Point Process, and some interest has developed over the years on the typical and average properties of thesolution in the limit n to ∞. This PhD thesis investigates this problem in a number of cases (many exact results in d=1, the derivation of some fine properties in d=2, in part still conjectural, an investigation on self-similar fractals with 1
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Submitted on : Monday, January 11, 2021 - 6:36:08 PM
Last modification on : Sunday, June 26, 2022 - 3:03:27 AM

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• HAL Id : tel-03098672, version 2

### Citation

Matteo d' Achille. Statistical properties of the Euclidean random assignment problem. Other Statistics [stat.ML]. Université Paris-Saclay, 2020. English. ⟨NNT : 2020UPASQ003⟩. ⟨tel-03098672v2⟩

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