### Abstract

For a finite metric space V with a metric ρ, let V^{n} be the metric space in which the distance between (a_{1}, . . ., a_{n}) and (b_{1}, . . ., b_{n}) is the sum ∑^{n}_{i=1} ρ(a_{i}, b_{i}). We obtain an asymptotic formula for the logarithm of the maximum possible number of points in V^{n} of distance at least d from a set of half the points of V^{n}, when n tends to infinity and d satisfies d ≫ √n.

Original language | English (US) |
---|---|

Pages (from-to) | 411-436 |

Number of pages | 26 |

Journal | Geometric and Functional Analysis |

Volume | 8 |

Issue number | 3 |

State | Published - 1998 |

### Fingerprint

### ASJC Scopus subject areas

- Mathematics(all)
- Analysis

### Cite this

*Geometric and Functional Analysis*,

*8*(3), 411-436.

**An asymptotic isoperimetric inequality.** / Alon, Noga; Boppana, Ravi; Spencer, Joel.

Research output: Contribution to journal › Article

*Geometric and Functional Analysis*, vol. 8, no. 3, pp. 411-436.

}

TY - JOUR

T1 - An asymptotic isoperimetric inequality

AU - Alon, Noga

AU - Boppana, Ravi

AU - Spencer, Joel

PY - 1998

Y1 - 1998

N2 - For a finite metric space V with a metric ρ, let Vn be the metric space in which the distance between (a1, . . ., an) and (b1, . . ., bn) is the sum ∑ni=1 ρ(ai, bi). We obtain an asymptotic formula for the logarithm of the maximum possible number of points in Vn of distance at least d from a set of half the points of Vn, when n tends to infinity and d satisfies d ≫ √n.

AB - For a finite metric space V with a metric ρ, let Vn be the metric space in which the distance between (a1, . . ., an) and (b1, . . ., bn) is the sum ∑ni=1 ρ(ai, bi). We obtain an asymptotic formula for the logarithm of the maximum possible number of points in Vn of distance at least d from a set of half the points of Vn, when n tends to infinity and d satisfies d ≫ √n.

UR - http://www.scopus.com/inward/record.url?scp=0032392337&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032392337&partnerID=8YFLogxK

M3 - Article

VL - 8

SP - 411

EP - 436

JO - Geometric and Functional Analysis

JF - Geometric and Functional Analysis

SN - 1016-443X

IS - 3

ER -