An Asymptotic Isoperimetric Inequality
نویسندگان
چکیده
For a finite metric space V with a metric ρ, let V n be the metric space in which the distance between (a1, . . . , an) and (b1, . . . , bn) is the sum ∑n i=1 ρ(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 , when n tends to infinity and d satisfies d √ n. 1 The Main Results Let V be a finite metric space with metric ρ and with probability measure μ. On the set V n define naturally the product probability measure μn(a1, . . . , an) = n ∏
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