We modify Talagrand's generic chaining method to obtain upper bounds for all
p-th moments of the supremum of a stochastic process. These bounds lead to an
estimate for the upper tail of the supremum with optimal deviation parameters.
We apply our procedure to improve and extend some known deviation inequalities
for suprema of unbounded empirical processes and chaos processes. As an
application we give a significantly simplified proof of the restricted isometry
property of the subsampled discrete Fourier transform.

我们使用 Talagrand 通用串联方法修改，为随机过程的所有 p 阶矩获得上界。我们将此过程应用于改进和扩展一些已知的偏差不等式，以便获得至上极限的上尾估计，同时具有最佳的偏差参数，其中包括未限制的经验过程和混沌过程的极限值。作为实践，我们提供了约束等距性质的明显简化证明，该质将离散傅立叶变换的子采样用于稀疏信号恢复。

泛链式下尾部界

Tail bounds via generic chaining

We present a new bound for suprema of a special type of chaos processes
indexed by a set of matrices, which is based on a chaining method. As
applications we show significantly improved estimates for the restricted
isometry constants of partial random circulant matrices and time-frequency
structured random matrices. In both cases the required condition on the number
$m$ of rows in terms of the sparsity $s$ and the vector length $n$ is $m
\gtrsim s \log^2 s \log^2 n$.

本文提出一种基于链式方法的特殊类型混沌过程的最大值界限，作为应用，展示了对于部分随机循环矩阵和时频结构随机矩阵的受限等距常数的显著改进估计。在两种情况下，基于稀疏度 s 和向量长度 n 的行数 m 的所需条件是 m≳s (log2 s) 2 (log2 n)。