Spectral Gap for log-Concave Probability Measures on the Real Line
Spectral Gap for log-Concave Probability Measures on the Real Line
复制标题
实线上对数凹概率测度的谱间隙
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
P. Fougères
中科院分区：
文献类型：
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作者：
P. Fougères
我们提出了一个简单的参数，以描述用于真实线上的对数符合概率度量的庞孔孔库氏常数（或光谱间隙的倒数）的确切顺序。该参数是中位数距离的平均值的平方。 Bobkov最近就测量的方差得出了类似的结果。他的方法是基于对Cheeger常数的研究。我们的观点完全不同，并利用了Muckenhoupt功能和凸功能集中的变异计算。
We propose a simple parameter to describe the exact order of the Poincare constant (or the inverse of the spectral gap) for a log-concave probability measure on the real line. This parameter is the square of the mean value of the distance to the median. Bobkov recently derived a similar result in terms of the variance of the measure. His approach was based on the study of the Cheeger constant. Our viewpoint is quite different and makes use of the Muckenhoupt functional and of a variational computation in the set of convex functions.