论文标题
与指数常数的脱钩不平等
Decoupling inequalities with exponential constants
论文作者
论文摘要
将不等式的不等式解耦，使随机对象的复杂依赖性结构可以通过独立随机变量理论的标准工具进行分析。我们研究了在随机变量下评估的矢量值均相多项式的脱钩不平等。我们专注于提供几何条件，以确保仅根据多项式的程度指数型具有良好常数的脱钩不平等。假设BANACH空间具有有限的Cotype，我们实现了将多项式与其相关的多线性操作员进行比较的经典脱钩不平等。在涉及的BANACH空间上的更强的几何假设下，我们还获得了随机多项式与其系数的完全独立的随机总和之间的非平衡性。最后，我们提出了脱钩的不平等现象，在多线性操作员中，仅涉及随机向量的两个独立副本（一个重复的$ M-1 $ times）。
Decoupling inequalities disentangle complex dependence structures of random objects so that they can be analyzed by means of standard tools from the theory of independent random variables. We study decoupling inequalities for vector-valued homogeneous polynomials evaluated at random variables. We focus on providing geometric conditions ensuring decoupling inequalities with good constants depending only exponentially on the degree of the polynomial. Assuming the Banach space has finite cotype we achieve this for classical decoupling inequalities that compare the polynomials with their associated multilinear operators. Under stronger geometric assumptions on the involved Banach spaces, we also obtain decoupling inequalities between random polynomials and fully independent random sums of their coefficients. Finally, we present decoupling inequalities where in the multilinear operator just two independent copies of the random vector are involved (one repeated $m-1$ times).
