An asymptotic isoperimetric inequality

Noga Alon, Ravi Boppana, Joel Spencer

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Pages (from-to)411-436
Number of pages26
JournalGeometric and Functional Analysis
Volume8
Issue number3
StatePublished - 1998

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Isoperimetric Inequality
Metric space
Asymptotic Formula
Logarithm
Infinity
Tend
Metric

ASJC Scopus subject areas

  • Mathematics(all)
  • Analysis

Cite this

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

In: Geometric and Functional Analysis, Vol. 8, No. 3, 1998, p. 411-436.

Research output: Contribution to journalArticle

Alon, N, Boppana, R & Spencer, J 1998, 'An asymptotic isoperimetric inequality', Geometric and Functional Analysis, vol. 8, no. 3, pp. 411-436.
Alon, Noga ; Boppana, Ravi ; Spencer, Joel. / An asymptotic isoperimetric inequality. In: Geometric and Functional Analysis. 1998 ; Vol. 8, No. 3. pp. 411-436.
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