Concentration of measure for classical Lie groups

2018/10/15 by Sergio L. Cacciatori, Cacciatori, S. L., Pietro Ursino +1
Computer Science · Mathematics · Medicine · #FOS: Mathematics #FOS: Physical sciences #General Topology (math.GN) #Group Theory (math.GR) #Mathematical Physics (math-ph) #Medical Imaging Techniques and Applications #Topological and Geometric Data Analysis #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1810.06492

openalex publication_date 2018/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Fundamentals of direct limit Lie theory

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