ASYMPTOTICS FOR TRANSPORTATION COST IN HIGH DIMENSIONS
ASYMPTOTICS FOR TRANSPORTATION COST IN HIGH DIMENSIONS
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DOI：
10.1007/bf02213456
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发表时间：
1995-01-01
影响因子：
0.8
通讯作者：
YUKICH, JE
中科院分区：
文献类型：
--
作者：
DOBRIC, V;YUKICH, JE
设X(1)，…，X(N)，Y-1，…，Y-n为I.I.D.设L(N)(Mu)=inf(Pi)Sigma(i=1)(N)平行于X(I)-Y-pi(I)，表示X和Y点的最优二部匹配，其中pi取值于整数1，2，…，n的所有排列，其中平行于的是R(D)上的范数。如果u是勒贝格测度，则证明了[GRAPHICS]，其中α是一个有限常数，依赖于平行于平行于且仅依赖于d。更一般地，对于任意的Mu，证明了[Graphics]，其中f是Mu的绝对连续部分的密度。我们还求出了收敛速度。
Let X(1),..., X(n), Y-1,..., Y-n be i.i.d. with the law mu on the cube [0,1](d), d greater than or equal to 3. Let L(n)(mu) = inf(pi)Sigma(i=1)(n) parallel to X(i) - Y-pi(i)parallel to denote the optimal bipartite matching of the X and Y points, where pi ranges over all permutations of the integers 1, 2,..., n, and where parallel to .parallel to is a norm on R(d). If mu is Lebesgue measure it is shown that[GRAPHICS]where alpha is a finite constant depending on parallel to parallel to and d only. More generally, for arbitrary mu it is shown that[GRAPHICS]where f is the density of the absolutely continuous part of mu. We also find the rate of convergence.