论文标题
GraphHörmander系统
Graph Hörmander Systems
论文作者
论文摘要
本文将连接RICCI曲率和Log-Sobolev的不等式的Bakry-émery定理扩展到矩阵值设置。使用非组合几何形状中的工具，可以表明，对于紧凑型谎言组的正确不变的二阶差分差异操作员，用于矩阵值修改的log-sobolev不平等的下限等效于所有有限尺寸表示的均匀下限。使用组合工具，我们使用组合方法获得了Graph-HörmanderSystems的矩阵值log-sobolev不平等的可计算下限。
This paper extends the Bakry-Émery theorem connecting the Ricci curvature and log-Sobolev inequalities to the matrix-valued setting. Using tools from noncommuative geometry, it is shown that for a right invariant second order differential operator on a compact Lie group, a lower bound for a matrix-valued modified log-Sobolev inequality is equivalent to a uniform lower bound for all finite dimensional representations. Using combinatorial tools, we obtain computable lower bounds for matrix-valued log-Sobolev inequalities of graph-Hörmander systems using combinatorial methods.
