This paper develops nonasymptotic growth and concentration bounds for a product of independent random matrices. These results sharpen and generalize recent work of Henriksen–Ward, and they are similar in spirit to the results of Ahlswede–Winter and of Tropp for a sum of independent random matrices. The argument relies on the uniform smoothness properties of the Schatten trace classes.

中文翻译：

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产品的基质浓度

本文为独立随机矩阵的乘积开发了非渐近增长和浓度界限。这些结果对 Henriksen-Ward 最近的工作进行了锐化和概括，它们在精神上与 Ahlswede-Winter 和 Tropp 的独立随机矩阵和的结果相似。该参数依赖于 Schatten 轨迹类的均匀平滑特性。