An asymptotic isoperimetric inequality

Noga Alon, Ravi Boppana, Joel Spencer

Research output: Contribution to journalArticle

19 Scopus citations

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
DOIs
StatePublished - Jan 1 1998
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Geometry and Topology

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