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 language | English (US) |
|---|---|
| Pages (from-to) | 411-436 |
| Number of pages | 26 |
| Journal | Geometric and Functional Analysis |
| Volume | 8 |
| Issue number | 3 |
| State | Published - 1998 |
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ASJC Scopus subject areas
- Mathematics(all)
- Analysis
Cite this
An asymptotic isoperimetric inequality. / Alon, Noga; Boppana, Ravi; Spencer, Joel.
In: Geometric and Functional Analysis, Vol. 8, No. 3, 1998, p. 411-436.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - An asymptotic isoperimetric inequality
AU - Alon, Noga
AU - Boppana, Ravi
AU - Spencer, Joel
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
UR - http://www.scopus.com/inward/citedby.url?scp=0032392337&partnerID=8YFLogxK
M3 - Article
VL - 8
SP - 411
EP - 436
JO - Geometric and Functional Analysis
JF - Geometric and Functional Analysis
SN - 1016-443X
IS - 3
ER -