### Abstract

This paper is devoted to the study of quotients of finite metric spaces. The basic type of question we ask is: Given a finite metric space M and α≥1, what is the largest quotient of (a subset of) M which well embeds into Hilbert space. We obtain asymptotically tight bounds for these questions, and prove that they exhibit phase transitions. We also study the analogous problem for embeddings into ℓ_{p}, and the particular case of the hypercube.

Original language | English (US) |
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Pages (from-to) | 451-494 |

Number of pages | 44 |

Journal | Advances in Mathematics |

Volume | 189 |

Issue number | 2 |

DOIs | |

State | Published - Dec 20 2004 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

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## Cite this

Mendel, M., & Naor, A. (2004). Euclidean quotients of finite metric spaces.

*Advances in Mathematics*,*189*(2), 451-494. https://doi.org/10.1016/j.aim.2003.12.001