论文标题
对数符号概率序列的几何和功能不平等现象
Geometric and Functional Inequalities for Log-concave Probability Sequences
论文作者
论文摘要
我们研究了对数符号概率序列类别的几何和功能不平等。我们证明了整数上的对数符号概率度量的扩张不平等。这种几何不平等的功能类似物被得出，从规律性的模量角度来看，与中位数的大小偏差不平等。我们的方法引起了独立的兴趣，我们发现对数式序列是属于单纯形半空间切片的对数孔串序列集的极端点。由于步行，gurvits和klartag-lehec，我们将此结果用作工具来得出几种卷积类型不等式的简单证明。我们结果的进一步应用用于生成Prékopa-Leindler不平等的离散版本。
We investigate geometric and functional inequalities for the class of log-concave probability sequences. We prove dilation inequalities for log-concave probability measures on the integers. A functional analogue of this geometric inequality is derived, giving large and small deviation inequalities from a median, in terms of a modulus of regularity. Our methods are of independent interest, we find that log-affine sequences are the extreme points of the set of log-concave sequences belonging to a half-space slice of the simplex. We use this result as a tool to derive simple proofs of several convolution type inequalities for log-concave sequences, due to Walkup, Gurvits, and Klartag-Lehec. Further applications of our results are used to produce a discrete version of the Prékopa-Leindler inequality.
