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

22 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 (US)
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 - 1998
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis
Geometry and Topology

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10.1007/s000390050062

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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.",

author = "Noga Alon and Ravi Boppana and Joel Spencer",

note = "Funding Information: The research of the rst author is supported in part by a USA{Israel BSF grant and by the Hermann Minkowski Minerva Center for Geometry at Tel Aviv University.",

year = "1998",

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pages = "411--436",

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T1 - An asymptotic isoperimetric inequality

AU - Alon, Noga

AU - Boppana, Ravi

AU - Spencer, Joel

N1 - Funding Information: The research of the rst author is supported in part by a USA{Israel BSF grant and by the Hermann Minkowski Minerva Center for Geometry at Tel Aviv University.

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.

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JO - Geometric and Functional Analysis

JF - Geometric and Functional Analysis

IS - 3

ER -

An asymptotic isoperimetric inequality

Abstract

All Science Journal Classification (ASJC) codes

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