### Abstract

We give a new proof of the classical central limit theorem, in the Mallows (L-r-Wasserstein) distance. Our proof is elementary in the sense that it does not require complex analysis, but rather makes use of a simple subadditive inequality related to this metric. The key is to analyse the case where equality holds. We provide some results concerning rates of convergence. We also consider convergence to stable distributions, and obtain a bound on the rate of such convergence.

Translated title of the contribution | Central limit theorem and convergence to stable laws in Mallows distance |
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Original language | English |

Pages (from-to) | 829 - 845 |

Number of pages | 17 |

Journal | Bernoulli |

Volume | 11 (5) |

Publication status | Published - Oct 2005 |

### Bibliographical note

Publisher: Int Statistical InstOther identifier: IDS number 976JH

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## Cite this

Johnson, OT., & Samworth, R. (2005). Central limit theorem and convergence to stable laws in Mallows distance.

*Bernoulli*,*11 (5)*, 829 - 845. http://isi.cbs.nl/bernoulli/abstracts/B04062abs115.pdf