Log-concave measures

Log-concave measures
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对数凹测度

DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
A. Üstünel
A. Üstünel
中科院分区：
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文献类型：
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作者：
D. Feyel;A. Üstünel

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研究了对数凹测度，利用Pr'ekopa-Leindler性质刻画了它们，并定义了一个子集，其元素称为超对数凹测度，这些超对数凹测度具有满足对数Sobolev不等式的性质.我们给出了它们的稳定性的一些结果。本文还指出了Monge-Kantorovitch方程和Monge-Kantorovitch方程与测度输运的某些关系及其应用。
We study the log-concave measures, their characterization via the Pr'ekopa-Leindler property and also define a subset of it whose elements are called super log-concave measures which have the property of satisfying a logarithmic Sobolev inequality. We give some results about their stability. Certain relations with measure transportation of Monge-Kantorovitch and the Monge-Amp'ere equation are also indicated with applications.