论文标题
随机参数化双张量积分及其应用
Random Parametrization Double Tensors Integrals and Their Applications
论文作者
论文摘要
在这项工作中，我们将双张量积分（DTI）从以前的工作扩展到参数化双张量积分（PDTI），通过将积分内核变换界限应用于上限PDTI标准并建立新的扰动公式。此外，研究了随机PDTI的收敛属性，并利用该特性来表征原始衍生张量与PDTI与原始衍生量张量的作用结果之间的关系。这些工具可帮助我们根据更普通的操作员不平等，例如亨氏不平等和Birman-Koplienko-Solomyak不平等的不平等，为随机张量的新尾部范围提供新的尾巴界限。此外，还根据我们的新衍生扰动公式和积分内核变换边界获得了有关随机张量的新尾部界限。
In this work, we extend double tensor integrals (DTI) from our previous work to parametrization double tensors integrals (PDTI) by applying integral kernel transform bounds to upper bound PDTI norm and establishing a new perturbation formula. Besides, the convergence property of random PDTI is investigated and this property is utilized to characterize the relation between the original derivative tensor and the action result of PDTI to the original derivative tensor. These tools help us to derive new tail bounds for random tensors according to more general operator inequalities, e.g., Heinz inequality and Birman-Koplienko-Solomyak inequality. Moreover, new tail bounds about random tensors are also obtained according to our new derived perturbation formula and integral kernel transform bounds.
