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.
Concentration of measure for classical Lie groups
Cacciatori S. L.
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2023-01-01
Abstract
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.
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