A remark on hypercontractivity and the concentration of measure phenomenon in a compact Riemannian manifold
A remark on hypercontractivity and the concentration of measure phenomenon in a compact Riemannian manifold
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关于紧黎曼流形中超收缩性和测度集中现象的评述
DOI：
10.1007/bf02764780
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发表时间：
1990
影响因子：
1
通讯作者：
M. Ledoux
中科院分区：
文献类型：
--
作者：
M. Ledoux
紧随着M. Gromov和V.D. Milman（1983）的拉普拉斯算子方法，我们稍微改进了他们对紧化riemann流形X的浓度函数α(X;ε)的一般估计，表明α(X;ε)≤C exp（−cε√ϱ0log(1+ε√ϱ0)）对于数值常数C， C >，其中ρ0 >是拉普拉斯onX的超压缩常数。
Following closely the Laplace operator method of M. Gromov and V.D. Milman (1983), we slightly improve their general estimate of the concentration functionα(X; ε) of a compact Riemannian manifold X by showing that α(X;ε)≦C exp(−cε√ϱ0log(1+ε√ϱ0)) for numerical constantsC, c > 0, whereρ0 > 0 is the hypercontractive constant of the Laplacian onX.