论文标题
布伦原理的随机形式
Stochastic forms of Brunn's principle
论文作者
论文摘要
最近已证明，由布鲁恩凹的原理引起的凸集的许多几何不平等现象产生了局部随机制剂。相比之下，在相关功能不平等的随机形式方面的进展要少得多。我们致力于凹函数的随机几何形状，以建立布伦原理的维度形式的局部版本A La Borell，Brascamp-Lieb和Rinott。为此，我们定义了凸面画像和射仪的阴影系统，并在多个积分重排不平等的背景下重新审视Rinott的方法。
A number of geometric inequalities for convex sets arising from Brunn's concavity principle have recently been shown to yield local stochastic formulations. Comparatively, there has been much less progress towards stochastic forms of related functional inequalities. We work towards a stochastic geometry of concave functions to establish local versions of dimensional forms of Brunn's principle a la Borell, Brascamp-Lieb, and Rinott. To do so, we define shadow systems of convex epigraphs and hypographs, and revisit Rinott's approach in the context of multiple integral rearrangement inequalities.
