Concentration of measure for classical Lie groups

We study the concentration of measure in metric-measurable (mm)-spaces. We define the notion of concentration locus of a flag sequence of metric-measurable (mm)-spaces. Some examples of infinite group action on an infinite dimensional compact and non-compact manifold show the role played by the trajectory of concentration locus. We also provide some applications in physics, which emphasize the role of concentration of measure in gravitational effects.

Automated summary

This paper examines the concentration of measure in metric-measurable (mm)-spaces, particularly focusing on the concentration locus of a flag sequence of such spaces. The trajectory of the concentration locus is illustrated through examples of infinite group action on infinite dimensional compact and non-compact manifolds. Furthermore, the paper discusses the significance of concentration of measure in gravitational effects, providing applications in physics.