论文标题
张量多元痕量不平等及其应用
Tensor Multivariate Trace Inequalities and their Applications
论文作者
论文摘要
我们证明了几种痕迹不平等，这些不平等扩展了Araki Lieb Terring（ALT）不平等，Golden Thompson（GT）的不平等和对数痕量不平等等于任意许多张量。我们的方法依赖于复杂的插值理论以及渐近光谱夹紧，提供了一种透明的机制来治疗通用张量的多元痕量不平等。作为我们张量扩展金汤普森不等式的张量扩展的示例应用，我们为张张量的独立总和提供了尾巴结合。这种约束将在高维概率和统计数据分析中发挥基本作用。
We prove several trace inequalities that extend the Araki Lieb Thirring (ALT) inequality, Golden Thompson (GT) inequality and logarithmic trace inequality to arbitrary many tensors. Our approaches rely on complex interpolation theory as well as asymptotic spectral pinching, providing a transparent mechanism to treat generic tensor multivariate trace inequalities. As an example application of our tensor extension of the Golden Thompson inequality, we give the tail bound for the independent sum of tensors. Such bound will play a fundamental role in high dimensional probability and statistical data analysis.
