An asymptotic isoperimetric inequality

Noga Alon; Ravi Boppana; Joel Spencer

doi:10.1007/s000390050062

An asymptotic isoperimetric inequality

Noga Alon, Ravi Boppana, Joel Spencer

Research output: Contribution to journal › Article › peer-review

23 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, . . ., a_n) and (b₁, . . ., 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 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 language	English
Pages (from-to)	411-436
Number of pages	26
Journal	Geometric and Functional Analysis
Volume	8
Issue number	3
DOIs	https://doi.org/10.1007/s000390050062
State	Published - 1 Jan 1998
Externally published	Yes

ASJC Scopus subject areas

Analysis
Geometry and Topology

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title = "An asymptotic isoperimetric inequality",

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.",

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AU - Spencer, Joel

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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.

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DO - 10.1007/s000390050062

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VL - 8

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EP - 436

JO - Geometric and Functional Analysis

JF - Geometric and Functional Analysis

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ER -

An asymptotic isoperimetric inequality

Abstract

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