TY - JOUR

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.

UR - http://www.scopus.com/inward/record.url?scp=0032392337&partnerID=8YFLogxK

U2 - 10.1007/s000390050062

DO - 10.1007/s000390050062

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AN - SCOPUS:0032392337

SN - 1016-443X

VL - 8

SP - 411

EP - 436

JO - Geometric and Functional Analysis

JF - Geometric and Functional Analysis

IS - 3

ER -