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

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 - Jan 1 1998

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ASJC Scopus subject areas

Analysis
Geometry and Topology

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Alon, N., Boppana, R., & Spencer, J. (1998). An asymptotic isoperimetric inequality. Geometric and Functional Analysis, 8(3), 411-436. https://doi.org/10.1007/s000390050062

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10.1007/s000390050062