论文标题
Dyson方程式的$ 2 $阳性地图和Hölder的界限
The Dyson equation for $2$-positive maps and Hölder bounds for the Lévy distance of densities of states
论文作者
论文摘要
所谓的状态密度是与我们在任何固定的$ c^\ ast $ - 启用空间上设置的dyson方程解决方案相关的实际线路上的borel概率度量，用于自换功能偏移和$ 2 $ probsitive的线性映射。使用来自游离非交通函数理论的技术，当两个参数中的任何一个变化时，我们证明了两个此类措施的Lévy距离的明确范围。作为证明的主要工具（也引起了独立的兴趣），我们表明dyson方程的解决方案具有强大的分析属性，并根据Inviscid Burgers方程的运营商价值版本沿任何$ 2 $ 2 $ 2 $ 2 $ 2 $ 2 $ 2的线性地图而发展。
The so-called density of states is a Borel probability measure on the real line associated with the solution of the Dyson equation which we set up, on any fixed $C^\ast$-probability space, for a selfadjoint offset and a $2$-positive linear map. Using techniques from free noncommutative function theory, we prove explicit Hölder bounds for the Lévy distance of two such measures when any of the two parameters varies. As the main tools for the proof, which are also of independent interest, we show that solutions of the Dyson equation have strong analytic properties and evolve along any $C^1$-path of $2$-positive linear maps according to an operator-valued version of the inviscid Burgers equation.
