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An Asymptotic Isoperimetric Inequality Ravi Boppana
 

Summary: An Asymptotic Isoperimetric Inequality
Noga Alon
Ravi Boppana
Joel Spencer
Abstract
For a finite metric space V with a metric , let V n
be the metric space in which the distance
between (a1, . . . , an) and (b1, . . . , bn) is the sum
n
i=1 (ai, bi). We obtain an asymptotic formula
for the logarithm of the maximum possible number of points in V n
of distance at least d from a
set of half the points of V n
, when n tends to infinity and d satisfies d

n.
1 The Main Results
Let V be a finite metric space with metric and with probability measure . On the set V n define
naturally the product probability measure
n(a1, . . . , an) =

  

Source: Alon, Noga - School of Mathematical Sciences, Tel Aviv University

 

Collections: Mathematics