Concentration of measure for classical Lie groups

TL;DR

This paper explores how measure concentrates in Lie group actions, introducing the concept of concentration locus and demonstrating its significance in infinite-dimensional settings and physics applications, especially gravity.

Contribution

It introduces the notion of concentration locus for Lie group sequences and illustrates its importance through examples and physics applications.

Findings

Concentration locus characterizes measure behavior in Lie group actions.

Infinite group actions influence measure concentration on manifolds.

Applications in physics highlight measure concentration's role in gravity phenomena.

Abstract

We study concentration of measure in Lie group actions. We define the notion of concentration locus of a flag sequence of Lie groups. 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.