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Fisher Information and Logarithmic Sobolev Inequality for Matrix-Valued Functions
Annales Henri Poincaré ( IF 1.5 ) Pub Date : 2020-09-25 , DOI: 10.1007/s00023-020-00947-9
Li Gao , Marius Junge , Nicholas LaRacuente

We prove a version of Talagrand’s concentration inequality for subordinated sub-Laplacians on a compact Riemannian manifold using tools from noncommutative geometry. As an application, motivated by quantum information theory, we show that on a finite-dimensional matrix algebra the set of self-adjoint generators satisfying a tensor stable modified logarithmic Sobolev inequality is dense.



中文翻译:

矩阵值函数的Fisher信息和对数Sobolev不等式

我们使用非交换几何中的工具,在紧凑的黎曼流形上证明了次拉普拉斯下级Talagrand集中不等式的一种形式。作为一种应用,受量子信息理论的启发,我们证明了在有限维矩阵代数上,满足张量稳定的改进对数Sobolev不等式的自伴生子集是稠密的。

更新日期:2020-09-25
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